Verhoeff algorithm - Revision history

Frodo Maximus: /* growthexperiments-addlink-summary-summary:2|0|0 */

2025-06-11T07:21:05Z

Link suggestions feature: 2 links added.

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	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.		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.

	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>		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>

	==Goals==		==Goals==
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	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'').		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'').

	The inverse table '''''inv''''' represents the multiplicative inverse of a digit, that is, the value that satisfies ''d''(''j'', ''inv''(''j'')) = 0.		The inverse table '''''inv''''' represents the [[multiplicative inverse]] of a digit, that is, the value that satisfies ''d''(''j'', ''inv''(''j'')) = 0.

	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'')).		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'')).

103.16.202.102 at 13:47, 30 May 2025

2025-05-30T13:47:01Z

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	The original number is valid if and only if {{tmath\|1=c = 0}}.		The original number is valid if and only if {{tmath\|1=c = 0}}.

	To generate a check digit, append a {{val\|0}}, perform the calculation: the correct check digit is {{tmath\|inv(c)}}.		To generate a check digit, append a {{val\|0}}, perform the calculation: the correct check digit is {{tmath\|inv(c)}}..

	== Examples ==		== Examples ==

Headbomb: ce

2024-11-28T21:25:38Z

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	\| title=Error Detecting Decimal Codes (Tract 29)		\| title=Error Detecting Decimal Codes (Tract 29)
	\| last=Verhoeff \|first=J.		\| last=Verhoeff \|first=J.
	\| journal=Zeitschrift Angewandte Mathematik und Mechanik \| publisher=The Mathematical Centre, Amsterdam		\| journal=Zeitschrift für Angewandte Mathematik und Mechanik \| publisher=The Mathematical Centre, Amsterdam
	\| year=1969		\| year=1969
	\| volume=51 \| issue=3 \| page=240 \| doi=10.1002/zamm.19710510323 \|bibcode=1971ZaMM...51..240N		\| volume=51 \| issue=3 \| page=240 \| doi=10.1002/zamm.19710510323 \|bibcode=1971ZaMM...51..240N

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

Altered template type. Add: page, issue, volume, journal. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Modular arithmetic | #UCB_Category 62/62

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	{{reflist\|refs=		{{reflist\|refs=
	<ref name="Verhoeff_1969">		<ref name="Verhoeff_1969">
	{{cite ~~book~~		{{cite journal
	\| title=Error Detecting Decimal Codes (Tract 29)		\| title=Error Detecting Decimal Codes (Tract 29)
	\| last=Verhoeff \|first=J.		\| last=Verhoeff \|first=J.
	\| publisher=The Mathematical Centre, Amsterdam		\| journal=Zeitschrift Angewandte Mathematik und Mechanik \| publisher=The Mathematical Centre, Amsterdam
	\| year=1969		\| year=1969
	\| doi=10.1002/zamm.19710510323 \|bibcode=1971ZaMM...51..240N		\| volume=51 \| issue=3 \| page=240 \| doi=10.1002/zamm.19710510323 \|bibcode=1971ZaMM...51..240N
	}}		}}
	</ref>		</ref>

GhostInTheMachine: Changing short description from "goal of finding a decimal code" to "Way to detect errors in decimal codes"

2024-04-23T07:31:44Z

Changing short description from "goal of finding a decimal code" to "Way to detect errors in decimal codes"

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	{{Short description\|~~goal~~ of ~~finding~~ a decimal ~~code~~}}		{{Short description\|Way to detect errors in decimal codes}}
	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.		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.

AIVOP: #article-add-desc

2024-04-22T22:20:08Z

#article-add-desc

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			{{Short description\|goal of finding a decimal code}}
	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.		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.

Suslindisambiguator: /* References */ added author link for Joseph Kirtland

2024-03-07T18:34:08Z

References: added author link for Joseph Kirtland

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	}}		}}
	</ref>		</ref>
	<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>		<ref name=Kirtland_2001>{{cite book \| title=Identification Numbers and Check Digit Schemes \|last=Kirtland \|first=Joseph \| author-link=Joseph Kirtland \|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>

	<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>		<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>

Artoria2e5: any base

2023-08-28T17:50:30Z

any base

← Previous revision		Revision as of 17:50, 28 August 2023
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	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.		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.

	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.<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>		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>

	==Goals==		==Goals==

Artoria2e5: Gumm

2023-08-28T17:47:03Z

Gumm

← Previous revision		Revision as of 17:47, 28 August 2023
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	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.		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.

			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.<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>

	==Goals==		==Goals==

Artoria2e5: See also

2023-08-28T17:43:52Z

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	''c'' is zero, so the check is correct.		''c'' is zero, so the check is correct.
	{{col-end}}		{{col-end}}

			== See also ==
			* [[Luhn algorithm]], earlier (1960) check digit algorithm

	== References ==		== References ==