https://en.wikipedia.org/w/index.php?action=history&feed=atom&title=Verhoeff_algorithm
Verhoeff algorithm - Revision history
2025-06-24T16:28:31Z
Revision history for this page on the wiki
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Frodo Maximus: /* growthexperiments-addlink-summary-summary:2|0|0 */
2025-06-11T07:21:05Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 07:21, 11 June 2025</td>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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<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>
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<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.<ref>{{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}}</ref></div></td>
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<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.<ref>{{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}}</ref></div></td>
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<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>
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<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<sub>5</sub>.<ref name=Gallian_2010 /> 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>
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<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<sub>5</sub>.<ref name=Gallian_2010 /> 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>
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<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>
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<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>
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<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>
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<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>
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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
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<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>
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103.16.202.102
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<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>
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<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>
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Citation bot
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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 "goal of finding a decimal code" to "Way to detect errors in decimal codes"</p>
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<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>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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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>
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<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>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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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>
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<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><ref name=Kirtland_2001>{{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&pg=PA121 }}</ref></div></td>
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<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><ref name=Kirtland_2001>{{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&pg=PA121 }}</ref></div></td>
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<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>
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<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><ref name=Salomon_2005>{{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&pg=PA57 }}</ref></div></td>
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<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><ref name=Salomon_2005>{{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&pg=PA57 }}</ref></div></td>
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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>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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<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'''<ref name="Verhoeff_1969" /> is a [[checksum]] for [[error detection]] first published by Dutch mathematician [[Jacobus Verhoeff]] in 1969.<ref name=Kirtland_2001 /><ref name=Salomon_2005 /> It was the first decimal [[check digit]] algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits,<ref name=Haunsperger_2006 /> which was at the time thought impossible with such a code.</div></td>
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<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>
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<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>.<ref>{{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}}</ref></div></td>
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<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.<ref>{{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}}</ref></div></td>
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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>
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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>
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Artoria2e5