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.<ref name=dhmd /><ref name=damm2007 /><ref group=lower-roman name=BIS2003 /><ref group=lower-roman name=Chen2009 /> Damm revealed several methods to create such TAtotally anti-symmetric quasigroups of order 10 and gave some examples in his doctoral dissertation.<ref name=dhmd /><ref group=lower-roman name=BIS2003 /> With this, Damm also disproved an old conjecture that TAtotally anti-symmetric quasigroups of order 10 do not exist.<ref name=damm2003 />

== Algorithm ==