|
On check digit systems using totally anti-symmetric quasigroups
by
Michael Damm
We consider check digit systems over a quasigroup (Q, *) of order m with check equation (...(xn*xn-1)*xn-2...)*x0=d. Such a system detects all single errors (i.e. one wrong digit); and it detects all adjacent transpositions (i.e. errors of the form ...ab... --> ...ba...) iff (Q, *) is totally anti-symmetric that means that (Q, *) fulfills the condition: x*y=y*x or (c*x)*y=(c*y)*x implies x=y. In this survey we report on the characteristics and the existence of totally anti-symmetric quasigroups. Using this in a fast algorithm we disprove a conjecture of Ecker&Poch that totally anti-symmetric quasigroups do not exist for m=4k+2.
Date received: January 1, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafo-42.