Reversible and Reversible Complement Cyclic codes over a class of non-chain rings

Nikita Jain; Sucheta Dutt; Ranjeet Sehmi

paper

Reversible and Reversible Complement Cyclic codes over a class of non-chain rings

arXiv:2304.02913

Abstract

In this paper, necessary and sufficient conditions for a cyclic code of arbitrary length over the non-chain rings $Z_{4} + ν Z_{4}$ for $ν^{2} \in {0, 1, ν, 2 ν, 3 ν, 2 + ν, 2 + 3 ν, 3 + 2 ν}$ to be a reversible cyclic code have been established. Also, conditions for a cyclic code over these non-chain rings to be a reversible complement cyclic code which are necessary as well as sufficient have been determined. Some examples of reversible and reversible complement cyclic codes over these rings have also been presented.