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|ISBN-10isbn]] [[Check_digit#ISBN_10|check digit]] scheme).
Prepending leading zeros does not affect the check digit.
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== References ==
{{reflist|refs=
<ref name=dhmd>{{cite book |last=Damm |dateyear=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 |id=[http://nbn-resolving.de/urn:nbn:de:hebis:04-z2004-05162 urn:nbn:de:hebis:04-z2004-05162]}}{{De icon}}</ref>
<ref name=damm2003>{{cite journal |last=Damm |dateyear=2003 |first=H. Michael |title=On the Existence of Totally Anti-Symmetric Quasigroups of Order 4''k'' + 2 |journal=Computing |volume=70 |issue=4 |pages=349–357 |url=http://link.springer.com/article/10.1007%2Fs00607-003-0017-3 |issn=0010-485X |doi=10.1007/s00607-003-0017-3 }}</ref>
<ref name=damm2007>{{cite journal |last=Damm |dateyear=2007 |first=H. Michael |title=Totally anti-symmetric quasigroups for all orders ''n''≠2,6 |journal=Discrete Mathematics |volume=307 |issue=6 |pages=715–729 |url=http://www.sciencedirect.com/science/article/pii/S0012365X06004225 |issn=0012-365X |doi=10.1016/j.disc.2006.05.033 }}</ref>
<ref name=Kirtland2001>{{cite book |last=Kirtland |dateyear=2001 |first=Joseph |title=Identification Numbers and Check Digit Schemes |publisher=Mathematical Association of America |series=Classroom Resource Materials |pages=4-54–5 |url=http://books.google.com/books?id=npTxORxmLosC&pg=PA4 |isbn=978-0-88385-720-5 }}</ref>
}}
{{reflist|group=lower-roman|refs=
<ref group=lower-roman name=BIS2003 >{{cite journal |dateyear=2003 |author1=[http://www.math.md/people/beliavscaia-galina/ Beliavscaia Galina] |author2=[http://www.math.md/people/izbas-vladimir/ Izbaş Vladimir] |author3=[http://www.math.md/people/scerbacov-victor/ Şcerbacov Victor] |title=Check character systems over quasigroups and loops |journal=[http://www.math.md/en/publications/qrs/ Quasigroups and Related Systems] |volume=10 |issue=[http://www.math.md/en/publications/qrs/issues/v10-n1/ 1] |pages=[http://www.math.md/en/publications/qrs/issues/v10-n1/10592/ 1-281–28] |url=http://www.math.md/files/qrs/v10-n1/v10-n1-(pp1-28).pdf |issn=1561-2848 }} See page 23.</ref>
<ref group=lower-roman name=Chen2009>{{cite book |author=Chen Jiannan |dateyear=2009 |chapter=The NP-completeness of Completing Partial anti-symmetric Latin squares |pages=[http://www.academypublisher.com/proc/iwisa09/papers/iwisa09p322.htm 322-324322–324] |chapter-url=http://www.academypublisher.com/proc/iwisa09/papers/iwisa09p322.pdf |title=Proceedings of 2009 International Workshop on Information Security and Application (IWISA 2009) |url=http://www.academypublisher.com/proc/iwisa09/ |editor1editor=Feng Gao |editor2=Xijun Zhu |publisher=[http://www.academypublisher.com/ Academy Publisher] |isbn=978-952-5726-06-0 }} See page 324.</ref>
