A check digit system over a group of arbitrary order

In this paper, we study a check digit system over an abelian group of an arbitrary order. The work is a generalization of a recently introduced check digit system which is based on the use of elementary abelian p-group of order p^k. Furthermore, we challenge the current standards by comparing our system with several well-known and widely used systems such as ISBN, MEID, ISAN and the system over alphanumeric characters. We show that our design outperforms all of them in terms of the error detection capability.