Damm algorithm: Difference between revisions

Revision as of 04:21, 18 January 2013

Revision as of 05:01, 18 January 2013

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== Strengths and weaknesses ==

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=dhmdKirtland2001 /> 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|ISBN-10]] [[Check_digit#ISBN_10|check digit]] scheme).

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<ref name=dhmd>{{cite book | last=Damm | date=2004 | first=H. Michael | title=Total anti-symmetrische Quasigruppen | type=Dr. rer. nat. | publisher=Philipps-Universität Marburg | url=http://archiv.ub.uni-marburg.de/diss/z2004/0516/pdf/dhmd.pdf }}</ref>

<ref name=damm2003>{{cite journal | last=Damm | date=2003 | first=H. Michael | title=On the Existence of Totally Anti-Symmetric Quasigroups of Order 4''k''&nbsp;+&nbsp;2 | journal=Computing | volume=70 | issue=4 | pages=349–357 | url=http://link.springer.com/article/10.1007%2Fs00607-003-0017-3 }}</ref>

<ref name=Kirtland2001>{{cite book | last=Kirtland | date=2001 | first=Joseph | title=Identification Numbers and Check Digit Schemes | publisher=Mathematical Association of America | series=Classroom Resource Materials | pages=4-5 | url=http://books.google.com/books?id=npTxORxmLosC&pg=PA4 | isbn=9780883857205 }}</ref>

}}

*{{cite journal | last=Damm | date=2007 | first=H. Michael | title=Totally anti-symmetric quasigroups for all orders ''n''&ne;2,6 | journal=Discrete Mathematics | volume=307 | issue=6 | pages=715–729 | url=http://www.sciencedirect.com/science/article/pii/S0012365X06004225 }}

== External links ==

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

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

{{DEFAULTSORT:Damm Algorithm}}