Cyclic and constacyclic codes over a non-chain ring

Abstract

In this study, we consider linear and especially cyclic codes over the non-chain ring $Z_{p}[v]/\langle v^{p}-v\rangle$ 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.