Repeated Root Constacyclic Codes of Length $m{p}^s$ over ${\mathbb{F}}_{p^r}+u{\mathbb{F}}_{p^r}+...+u^{e-1}{\mathbb{F}}_{p^r}$

Abstract

We give the structure of $\lambda$-constacyclic codes of length $p^{s}m$ over $R={\mathbb{F}}_{p^r}+u{\mathbb{F}}_{p^r}+...+u^{e-1}{\mathbb{F}}_{p^r}$ with $λ\in \F_{p^r}^*$. We also give the structure of $\lambda$-constacyclic codes of length $p^{s}m$ with $\lambda ={\alpha }_1+u{\alpha }_2+...+u^{e-1}{\alpha }_{e-1}$, where ${\alpha }_1,{\alpha }_2\ne 0$ and study the self-duality of these codes.