Skew cyclic codes over F_{p}+uF_{p}+\dots +u^{k-1}F_{p}

TL;DR

This paper investigates skew cyclic codes over a specific ring extension of finite fields, characterizing their structure, generators, and providing algorithms for encoding and decoding.

Contribution

It introduces a comprehensive characterization of skew cyclic codes over R_{k} and develops algorithms for their encoding and decoding processes.

Findings

Characterization of skew cyclic codes as free modules

Construction of generators and minimal generating sets

Development of encoding and decoding algorithms

Abstract

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle x^{n}-1\rangle and construct their generators and minimal generating sets. Also, an algorithm has been provided to encode and decode these skew cyclic codes.