Damm Algorithm

The Damm algorithm is a check digit method for detecting errors in strings of digits, created by H. Michael Damm and presented in his 2004 doctoral dissertation, Totally Antisymmetric Quasigroups. It detects all single-digit errors and all errors caused by transposing two adjacent digits. Its error-detecting power is similar to the older Verhoeff algorithm, but the Damm algorithm needs no specially constructed permutation tables and, because it always produces a digit from 0 to 9, it never requires a non-digit check character of the kind used in ISBN-10 check digits. The algorithm rests on a mathematical structure called a weakly totally anti-symmetric quasigroup of order 10, and that structure is what gives the method its error-detection guarantees.