Skew constacyclic codes over Fq+uFq+vFq

TL;DR

This paper investigates skew constacyclic codes over a specific finite ring, revealing their structural properties and relationships to other code types, with implications for code construction over finite fields.

Contribution

It introduces the structure and properties of skew constacyclic codes over a non-chain ring and connects their Gray images to skew quasi-cyclic codes over finite fields.

Findings

Gray image of skew alpha-constacyclic code is a skew alpha-quasi-cyclic code over F_q

Skew alpha-constacyclic codes are equivalent to alpha-constacyclic or alpha-quasi-twisted codes over R

Structural properties are derived via decomposition method

Abstract

In this paper skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv = vu = 0 are studied. We show that Gray image of a skew alpha-constacyclic cyclic code of length n over R is a skew alpha-quasi-cyclic code of length $3n$ over F_{q} of index 3. It is also shown that skew alpha-constacyclic codes are either equivalent to alpha-constacyclic codes or alpha-quasi-twisted codes over R. Further, the structural properties of skew constacyclic over R are obtained by decomposition method.