Linear and cyclic codes over some special rings

Abstract

In this paper, we describe linear and cyclic codes over the rings of the form $R_{s,p}={\mathbb{Z}}_p[u]/\left(f\left(u\right)/\left(u-s\right)\right)$, where $p$ is a prime number and $f\left(u\right)=u^p-u$, with $s\in \{0,1,...,p-1\}$.