Cyclic and constacyclic codes over a non-chain ring

In this study, we consider linear and especially cyclic codes over the non-chain ring Zp[υ] / υ^p - υ where p is a prime. This is a generalization of the case p = 3: Further, in this work the structure of constacyclic codes are studied as well. This study takes advantage mainly from a Gray map which preserves the distance between codes over this ring and p-ary codes and moreover this map enlightens the structure of these codes. Furthermore, a MacWilliams type identity is presented together with some illustrative examples.