It was presented by H. Michael Damm in 2004,[1] as a part of his PhD dissertation entitled Totally Antisymmetric Quasigroups.
[1][2] The Damm algorithm has the benefit that it does not have the dedicatedly constructed permutations and its position-specific powers of the Verhoeff scheme.
The Damm algorithm generates only 10 possible values, avoiding the need for a non-digit character (such as the X in the 10-digit ISBN check digit scheme).
Prepending leading zeros does not affect the check digit (a weakness for variable-length codes).
Its essential part is a quasigroup of order 10 (i.e. having a 10 × 10 Latin square as the body of its operation table) with the special feature of being weakly totally anti-symmetric.
[3][4][i][ii][iii] Damm revealed several methods to create totally anti-symmetric quasigroups of order 10 and gave some examples in his doctoral dissertation.