On constacyclic codes over a class of non-chain rings

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.