Damm algorithm: Difference between revisions

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{{Short description|Check digit algorithm}}

In [[error detection]], the '''Damm algorithm''' is a [[check digit]] [[algorithm]] that detects all [[Transcription error|single-digit errors]] and all [[Transcription error#Transposition error|adjacent transposition errors]]. It was presented by H. Michael Damm in 2004.,<ref name="fenwick2014" /> as a part of his PhD dissertation entitled ''Totally Antisymmetric Quasigroups.''

== Strengths and weaknesses ==

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== Example ==

The following operation table will be used.<ref name="fenwick2014" /> It may be obtained from the totally anti-symmetric quasigroup {{math|''x'' ∗ ''y''}} in Damm's doctoral dissertation page 111<ref name="dhmd" /> by rearranging the rows and changing the entries with the permutation {{math|1=''φ'' = (1&nbsp;2&nbsp;9&nbsp;5&nbsp;4&nbsp;8&nbsp;6&nbsp;7&nbsp;3)}} and defining {{math|1=''x'' ⋅ ''y'' = ''φ''^&minus;1(''φ''(''x'') ∗ ''y'')}}.

{| class="skin-invert wikitable" style="text-align:center;background:none;color:#E000E0"

|- style="color:#00A000"

|style="width:1.5em"| {{math|1=⋅}}

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=== Calculating the check digit ===

{| class="skin-invert wikitable" style="text-align:center;background:none;color:#E000E0"

|- style="color:#00A000"

!style="color:black"| <span style="color:#00A000">digit to be processed</span> → column index

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=== Validating a number against the included check digit ===

{| class="skin-invert wikitable" style="text-align:center;background:none;color:#E000E0"

|- style="color:#00A000"

!style="color:black"| <span style="color:#00A000">digit to be processed</span> → column index

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|style="width:1.5em"| 7

|style="width:1.5em"| 2

|

|style="width:1.5em"| 4

|-

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| 9

| 7

|

| 4

|-

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| 7

| 4

|

| '''0'''

|}

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{{Wikibooks|Algorithm Implementation/Checksums/Damm Algorithm}}

*[[b:Algorithm Implementation/Checksums/Damm Algorithm|Damm validation & generation code in several programming languages]]

*[httphttps://blogwww.cantab-ip.com/blog/2014/01/20/new-format-for-singapore-ip-application-numbers-at-ipos/ Practical application in Singapore]

*[http://www.md-software.de/math/DAMM_Quasigruppen.txt Quasigroups for the Damm algorithm up to order 64]

*[https://rosettacode.org/wiki/Damm_algorithm At RosettaCode.org, Implementations of the Damm algorithm in many programming languages]