https://en.wikipedia.org/w/index.php?action=history&feed=atom&title=Verhoeff_algorithm Verhoeff algorithm - Revision history 2025-06-24T18:38:47Z Revision history for this page on the wiki MediaWiki 1.45.0-wmf.6 https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1295028151&oldid=prev Frodo Maximus: /* growthexperiments-addlink-summary-summary:2|0|0 */ 2025-06-11T07:21:05Z <p>Link suggestions feature: 2 links added.</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:21, 11 June 2025</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to any base.&lt;ref&gt;{{cite journal |last1=Gumm |first1=H. |title=A new class of check-digit methods for arbitrary number systems (Corresp.) |journal=IEEE Transactions on Information Theory |date=January 1985 |volume=31 |issue=1 |pages=102–105 |doi=10.1109/TIT.1985.1056991 |url=https://www.researchgate.net/publication/3084126}}&lt;/ref&gt;</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The method was independently discovered by H. Peter Gumm in 1985, this time including a <ins style="font-weight: bold; text-decoration: none;">[[</ins>formal proof<ins style="font-weight: bold; text-decoration: none;">]]</ins> and an extension to any base.&lt;ref&gt;{{cite journal |last1=Gumm |first1=H. |title=A new class of check-digit methods for arbitrary number systems (Corresp.) |journal=IEEE Transactions on Information Theory |date=January 1985 |volume=31 |issue=1 |pages=102–105 |doi=10.1109/TIT.1985.1056991 |url=https://www.researchgate.net/publication/3084126}}&lt;/ref&gt;</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Goals==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Goals==</div></td> </tr> <tr> <td colspan="2" class="diff-lineno">Line 253:</td> <td colspan="2" class="diff-lineno">Line 253:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The first table, '''''d''''', is based on multiplication in the dihedral group D&lt;sub&gt;5&lt;/sub&gt;.&lt;ref name=Gallian_2010 /&gt; and is simply the [[Cayley table]] of the group. Note that this group is not [[commutative]], that is, for some values of ''j'' and ''k'', ''d''(''j'',''k'') ≠ ''d''(''k'', ''j'').</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The first table, '''''d''''', is based on multiplication in the dihedral group D&lt;sub&gt;5&lt;/sub&gt;.&lt;ref name=Gallian_2010 /&gt; and is simply the [[Cayley table]] of the group. Note that this group is not [[commutative]], that is, for some values of ''j'' and ''k'', ''d''(''j'',''k'') ≠ ''d''(''k'', ''j'').</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The inverse table '''''inv''''' represents the multiplicative inverse of a digit, that is, the value that satisfies ''d''(''j'', ''inv''(''j'')) = 0.</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The inverse table '''''inv''''' represents the <ins style="font-weight: bold; text-decoration: none;">[[</ins>multiplicative inverse<ins style="font-weight: bold; text-decoration: none;">]]</ins> of a digit, that is, the value that satisfies ''d''(''j'', ''inv''(''j'')) = 0.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The permutation table '''''p''''' applies a [[permutation]] to each digit based on its position in the number. This is actually a single permutation {{nowrap|(1 5 8 9 4 2 7 0)(3 6)}} applied iteratively; i.e. ''p''(''i''+''j'',''n'') = ''p''(''i'', ''p''(''j'',''n'')).</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The permutation table '''''p''''' applies a [[permutation]] to each digit based on its position in the number. This is actually a single permutation {{nowrap|(1 5 8 9 4 2 7 0)(3 6)}} applied iteratively; i.e. ''p''(''i''+''j'',''n'') = ''p''(''i'', ''p''(''j'',''n'')).</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1293067978:rev-1295028151:wikidiff2=table:1.14.1:ff290eae --> </table> Frodo Maximus https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1293067978&oldid=prev 103.16.202.102 at 13:47, 30 May 2025 2025-05-30T13:47:01Z <p></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:47, 30 May 2025</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 265:</td> <td colspan="2" class="diff-lineno">Line 265:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The original number is valid if and only if {{tmath|1=c = 0}}.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The original number is valid if and only if {{tmath|1=c = 0}}.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>To generate a check digit, append a {{val|0}}, perform the calculation: the correct check digit is {{tmath|inv(c)}}.</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>To generate a check digit, append a {{val|0}}, perform the calculation: the correct check digit is {{tmath|inv(c)}}<ins style="font-weight: bold; text-decoration: none;">.</ins>.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Examples ==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Examples ==</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1260103021:rev-1293067978:wikidiff2=table:1.14.1:ff290eae --> </table> 103.16.202.102 https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1260103021&oldid=prev Headbomb: ce 2024-11-28T21:25:38Z <p>ce</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 21:25, 28 November 2024</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 316:</td> <td colspan="2" class="diff-lineno">Line 316:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| title=Error Detecting Decimal Codes (Tract 29)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| title=Error Detecting Decimal Codes (Tract 29)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| last=Verhoeff |first=J.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| last=Verhoeff |first=J.</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| journal=Zeitschrift Angewandte Mathematik und Mechanik | publisher=The Mathematical Centre, Amsterdam</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| journal=Zeitschrift<ins style="font-weight: bold; text-decoration: none;"> für</ins> Angewandte Mathematik und Mechanik | publisher=The Mathematical Centre, Amsterdam</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| year=1969</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| year=1969</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| volume=51 | issue=3 | page=240 | doi=10.1002/zamm.19710510323 |bibcode=1971ZaMM...51..240N</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| volume=51 | issue=3 | page=240 | doi=10.1002/zamm.19710510323 |bibcode=1971ZaMM...51..240N</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1251662456:rev-1260103021:wikidiff2=table:1.14.1:ff290eae --> </table> Headbomb https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1251662456&oldid=prev Citation bot: Altered template type. Add: page, issue, volume, journal. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Modular arithmetic | #UCB_Category 62/62 2024-10-17T10:11:58Z <p>Altered template type. Add: page, issue, volume, journal. | <a href="/wiki/Wikipedia:UCB" class="mw-redirect" title="Wikipedia:UCB">Use this bot</a>. <a href="/wiki/Wikipedia:DBUG" class="mw-redirect" title="Wikipedia:DBUG">Report bugs</a>. | Suggested by Dominic3203 | <a href="/wiki/Category:Modular_arithmetic" title="Category:Modular arithmetic">Category:Modular arithmetic</a> | #UCB_Category 62/62</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:11, 17 October 2024</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 313:</td> <td colspan="2" class="diff-lineno">Line 313:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{reflist|refs=</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{reflist|refs=</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ref name="Verhoeff_1969"&gt;</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ref name="Verhoeff_1969"&gt;</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{cite <del style="font-weight: bold; text-decoration: none;">book</del></div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{cite <ins style="font-weight: bold; text-decoration: none;">journal</ins></div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| title=Error Detecting Decimal Codes (Tract 29)</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| title=Error Detecting Decimal Codes (Tract 29)</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| last=Verhoeff |first=J.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| last=Verhoeff |first=J.</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| publisher=The Mathematical Centre, Amsterdam</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| journal=Zeitschrift Angewandte Mathematik und Mechanik </ins>| publisher=The Mathematical Centre, Amsterdam</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| year=1969</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>| year=1969</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| doi=10.1002/zamm.19710510323 |bibcode=1971ZaMM...51..240N</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">| volume=51 | issue=3 | page=240 </ins>| doi=10.1002/zamm.19710510323 |bibcode=1971ZaMM...51..240N</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/ref&gt;</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/ref&gt;</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1220353290:rev-1251662456:wikidiff2=table:1.14.1:ff290eae --> </table> Citation bot https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1220353290&oldid=prev GhostInTheMachine: Changing short description from "goal of finding a decimal code" to "Way to detect errors in decimal codes" 2024-04-23T07:31:44Z <p>Changing <a href="/wiki/Wikipedia:Short_description" title="Wikipedia:Short description">short description</a> from &quot;goal of finding a decimal code&quot; to &quot;Way to detect errors in decimal codes&quot;</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:31, 23 April 2024</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{Short description|<del style="font-weight: bold; text-decoration: none;">goal</del> <del style="font-weight: bold; text-decoration: none;">of</del> <del style="font-weight: bold; text-decoration: none;">finding</del> <del style="font-weight: bold; text-decoration: none;">a</del> decimal <del style="font-weight: bold; text-decoration: none;">code</del>}}</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Short description|<ins style="font-weight: bold; text-decoration: none;">Way</ins> <ins style="font-weight: bold; text-decoration: none;">to</ins> <ins style="font-weight: bold; text-decoration: none;">detect</ins> <ins style="font-weight: bold; text-decoration: none;">errors in</ins> decimal <ins style="font-weight: bold; text-decoration: none;">codes</ins>}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1220296020:rev-1220353290:wikidiff2=table:1.14.1:ff290eae --> </table> GhostInTheMachine https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1220296020&oldid=prev AIVOP: #article-add-desc 2024-04-22T22:20:08Z <p>#article-add-desc</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:20, 22 April 2024</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{Short description|goal of finding a decimal code}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1212410370:rev-1220296020:wikidiff2=table:1.14.1:ff290eae --> </table> AIVOP https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1212410370&oldid=prev Suslindisambiguator: /* References */ added author link for Joseph Kirtland 2024-03-07T18:34:08Z <p><span class="autocomment">References: </span> added author link for Joseph Kirtland</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:34, 7 March 2024</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 320:</td> <td colspan="2" class="diff-lineno">Line 320:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/ref&gt;</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/ref&gt;</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;ref name=Kirtland_2001&gt;{{cite book | title=Identification Numbers and Check Digit Schemes |last=Kirtland |first=Joseph | publisher=Mathematical Association of America | year=2001 | page=153 | isbn=0-88385-720-0 |chapter=5. Group Theory and the Verhoeff Check Digit Scheme | chapter-url=https://books.google.com/books?id=npTxORxmLosC&amp;pg=PA121 }}&lt;/ref&gt;</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;ref name=Kirtland_2001&gt;{{cite book | title=Identification Numbers and Check Digit Schemes |last=Kirtland |first=Joseph | <ins style="font-weight: bold; text-decoration: none;">author-link=Joseph Kirtland |</ins>publisher=Mathematical Association of America | year=2001 | page=153 | isbn=0-88385-720-0 |chapter=5. Group Theory and the Verhoeff Check Digit Scheme | chapter-url=https://books.google.com/books?id=npTxORxmLosC&amp;pg=PA121 }}&lt;/ref&gt;</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ref name=Salomon_2005&gt;{{cite book | title=Coding for Data and Computer Communications | last=Salomon |first=David | publisher=Springer | year=2005 | isbn=0-387-21245-0 |pages=56–58 |chapter=§2.11 The Verhoeff Check Digit Method | chapter-url=https://books.google.com/books?id=A88kvYwIVu0C&amp;pg=PA57 }}&lt;/ref&gt;</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;ref name=Salomon_2005&gt;{{cite book | title=Coding for Data and Computer Communications | last=Salomon |first=David | publisher=Springer | year=2005 | isbn=0-387-21245-0 |pages=56–58 |chapter=§2.11 The Verhoeff Check Digit Method | chapter-url=https://books.google.com/books?id=A88kvYwIVu0C&amp;pg=PA57 }}&lt;/ref&gt;</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1172690627:rev-1212410370:wikidiff2=table:1.14.1:ff290eae --> </table> Suslindisambiguator https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1172690627&oldid=prev Artoria2e5: any base 2023-08-28T17:50:30Z <p>any base</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:50, 28 August 2023</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to <del style="font-weight: bold; text-decoration: none;">more than</del> base<del style="font-weight: bold; text-decoration: none;"> 10</del>.&lt;ref&gt;{{cite journal |last1=Gumm |first1=H. |title=A new class of check-digit methods for arbitrary number systems (Corresp.) |journal=IEEE Transactions on Information Theory |date=January 1985 |volume=31 |issue=1 |pages=102–105 |doi=10.1109/TIT.1985.1056991 |url=https://www.researchgate.net/publication/3084126}}&lt;/ref&gt;</div></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to <ins style="font-weight: bold; text-decoration: none;">any</ins> base.&lt;ref&gt;{{cite journal |last1=Gumm |first1=H. |title=A new class of check-digit methods for arbitrary number systems (Corresp.) |journal=IEEE Transactions on Information Theory |date=January 1985 |volume=31 |issue=1 |pages=102–105 |doi=10.1109/TIT.1985.1056991 |url=https://www.researchgate.net/publication/3084126}}&lt;/ref&gt;</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Goals==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Goals==</div></td> </tr> </table> Artoria2e5 https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1172690108&oldid=prev Artoria2e5: Gumm 2023-08-28T17:47:03Z <p>Gumm</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:47, 28 August 2023</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The '''Verhoeff algorithm'''&lt;ref name="Verhoeff_1969" /&gt; is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.&lt;ref name=Kirtland_2001 /&gt;&lt;ref name=Salomon_2005 /&gt; It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,&lt;ref name=Haunsperger_2006 /&gt; which was at the time thought impossible with such a code.</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The method was independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to more than base 10.&lt;ref&gt;{{cite journal |last1=Gumm |first1=H. |title=A new class of check-digit methods for arbitrary number systems (Corresp.) |journal=IEEE Transactions on Information Theory |date=January 1985 |volume=31 |issue=1 |pages=102–105 |doi=10.1109/TIT.1985.1056991 |url=https://www.researchgate.net/publication/3084126}}&lt;/ref&gt;</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Goals==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Goals==</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1172689666:rev-1172690108:wikidiff2=table:1.14.1:ff290eae --> </table> Artoria2e5 https://en.wikipedia.org/w/index.php?title=Verhoeff_algorithm&diff=1172689666&oldid=prev Artoria2e5: See also 2023-08-28T17:43:52Z <p>See also</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Previous revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 17:43, 28 August 2023</td> </tr><tr> <td colspan="2" class="diff-lineno">Line 303:</td> <td colspan="2" class="diff-lineno">Line 303:</td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''c'' is zero, so the check is correct.</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>''c'' is zero, so the check is correct.</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{col-end}}</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{col-end}}</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td> </tr> <tr> <td colspan="2" class="diff-empty diff-side-deleted"></td> <td class="diff-marker" data-marker="+"></td> <td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* [[Luhn algorithm]], earlier (1960) check digit algorithm</div></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td> </tr> <tr> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td> <td class="diff-marker"></td> <td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References ==</div></td> </tr> <!-- diff cache key enwiki:diff:1.41:old-1170982803:rev-1172689666:wikidiff2=table:1.14.1:ff290eae --> </table> Artoria2e5