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.

19pages