On constacyclic codes over a class of non-chain rings

TL;DR

This paper investigates the structure and properties of constacyclic codes over a specific non-chain ring, providing generator forms, rank, cardinality, and conditions for reversibility, supported by illustrative examples.

Contribution

It introduces a unique generator form for constacyclic codes over a non-chain ring and determines conditions for their reversibility, expanding understanding of such codes.

Findings

Derived a unique generator form for these codes.

Established rank and cardinality formulas.

Provided necessary and sufficient conditions for reversibility.

Abstract

In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}=Z_{4}+\nu Z_{4}, \nu^{2}=\theta \in Z_{4}+\nu Z_{4}$ has been obtained. Further, rank and cardinality of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}$ have been obtained by determining a minimal spanning set of the code. Also, necessary and sufficient conditions for a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}$ to be reversible have been determined. Examples have also been presented in support of our results.