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

TL;DR

This paper characterizes the structure of repeated root constacyclic codes of length $mp^s$ over a specific finite chain ring, including their self-duality properties, extending the understanding of such codes in algebraic coding theory.

Contribution

It provides a detailed structural description of $ ext{lambda}$-constacyclic codes over a finite chain ring for various $ ext{lambda}$, including cases with non-unit coefficients, and analyzes their self-duality.

Findings

Explicit structure of $ ext{lambda}$-constacyclic codes over the ring.

Conditions for self-duality of these codes.

Extension of known results to more general $ ext{lambda}$ values.

Abstract

We give the structure of $\lambda$-constacyclic codes of length $p^sm$ over $R=\mathbb{F}_{p^r}+u \mathbb{F}_{p^r}+...+ u^{e-1}\mathbb{F}_{p^r}$ with $\lambda \in \F_{p^r}^*$. We also give the structure of $\lambda$-constacyclic codes of length $p^sm$ with $\lambda=\alpha_1+u\alpha_2+...+u^{e-1} \alpha_{e-1}$, where $\alpha_1,\alpha_2 \neq 0$ and study the self-duality of these codes.