Damm algorithm: Difference between revisions

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The Damm algorithm is similar to the [[Verhoeff algorithm]]. It too will detect ''all'' occurrences of the two most frequently appearing types of [[transcription error]]s, namely altering one single digit, and transposing two adjacent digits (including the transposition of the trailing check digit and the preceding digit).<ref name="fenwick2014" /><ref name="Salomon2005" /> 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 main 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 10ISBN_10|check digit]] scheme).
 
Prepending leading zeros does not affect the check digit.<ref name="fenwick2014" />