On cyclic codes over the ring $Z_p+u{Z}_p+...+u^{k-1}{Z}_p$

Abstract

In this paper, we study cyclic codes over the ring ${\mathbb{Z}}_p+u{\mathbb{Z}}_p+...+u^{k-1}{\mathbb{Z}}_p$, where $u^k=0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.