Reversible DNA codes over a family of non-chain rings $R_{k,s}$

Abstract

In this work we extend results introduced in [15]. Especially, we solve the reversibility problem for DNA codes over the non chain ring R k,s = F 4 2k [u1, . . . , us]/ u 2 1 − u1, . . . , u 2 s − us . We define an automorphism θ over R k,s which helps us both finding the idempotent decomposition of R k,s and solving the reversibility problem via skew cyclic codes. Moreover, we introduce a generalized Gray map that preserves DNA reversibility.