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

Abstract: In this paper, necessary and sufficient conditions for a cyclic code of arbitrary length over the non-chain rings $Z_{4}+\nu Z_{4}$ for $\nu^{2} \in {0,1,\nu,2\nu,3\nu,2+\nu,2+3\nu,3+2\nu}$ 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.