Damm algorithm: Difference between revisions

Revision as of 20:15, 9 January 2014

Revision as of 09:45, 5 May 2014

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=== Graphical illustration ===

This is the above example showing the detail of the algorithm generating the check digit (broken blue arrow) and verifying the number '''572''' with the check digit.

[[File:Check digit TA quasigroup dhmd111rr illustration eg5724.svg]]

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The Damm algorithm is similar to the [[Verhoeff algorithm]]. It too will detect ''all'' occurrences of altering one single digit and ''all'' occurrences of transposing two adjacent digits. (These are the two most frequently appearing types of [[transcription error]]s.)<ref name=Kirtland2001 /> But the Damm algorithm has the benefit that it makes do without the dedicatedly constructed [[permutation]]s and its position specific [[Exponentiation#In abstract algebra|powers]] being inherent in the [[Verhoeff algorithm|Verhoeff scheme]]. Furthermore, a table of [[Inverse element|inverses]] can be dispensed with provided all diagonal entries of the operation table are zero.

The Damm algorithm does not suffer from exceeding the number of 10 possible values, resulting in the need for using a non-digit character (as the [[X]] in the [[ISBN#ISBN-10 check digit calculation|10-digit ISBN]] [[Check digit#ISBN 10|check digit]] scheme).

Prepending leading zeros does not affect the check digit.