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

TL;DR

This paper addresses the reversibility of DNA codes over a specific non-chain ring by defining automorphisms and Gray maps, enabling the construction of reversible DNA codes with algebraic methods.

Contribution

It introduces a new approach using automorphisms and Gray maps to solve the reversibility problem for DNA codes over non-chain rings.

Findings

Reversibility problem solved for DNA codes over $R_{k,s}$.

Automorphism $ heta$ aids in idempotent decomposition and code analysis.

Generalized Gray map preserves DNA reversibility.

Abstract

In this paper, we solve the reversibility problem for DNA codes over the non-chain ring $R_{k,s}=\mathbb{F}_{4^{2k}}[u_1,...,u_{s}]/< u_1^2-u_1,..., u_s^2-u_s>$. We define an automorphism $\theta$ over $R_{k,s}$ which help us both find the idempotent decomposition of $R_{k,s}$ and solve the reversibility problem via skew cyclic codes. Moreover, we introduce a generalized Gray map that preserves DNA reversibility.