Damm algorithm: Difference between revisions

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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. Its essential part is a [[quasigroup]] of [[Order (group theory)|order]] 10 (i.e. having a 10×10 [[Latin square]] as [[Cayley table|operation table]]) with the special feature of being totally anti-symmetric. Damm revealed several methods to create such TA-quasigroups of order 10 and gave some examples in his doctoral dissertation.<ref name=dhmd>Damm, H. Michael (2004). ''[http://archiv.ub.uni-marburg.de/diss/z2004/0516/pdf/dhmd.pdf Total anti-symmetrische Quasigruppen (Dr. rer. nat.).]'' Philipps-Universität Marburg.</ref> With this, Damm also disproved an old conjecture that TA-quasigroups of order 10 do not exist.<ref>Damm, H.name=damm2003 Michael (2003). [http://link.springer.com/article/10.1007%2Fs00607-003-0017-3 "On the Existence of Totally Anti-Symmetric Quasigroups of Order 4''k''&nbsp;+&nbsp;2"] ''Computing'' '''70''' (4): 349–357.</ref>

== Algorithm ==

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== References ==

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<references />

<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>

*Damm, H. Michael (2007). [http://www.sciencedirect.com/science/article/pii/S0012365X06004225 "Totally anti-symmetric quasigroups for all orders ''n''&ne;2,6"] ''Discrete Mathematics'' '''307''' (6): 715–729.

<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>

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*{{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 }}

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