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Reversible DNA codes over a family of non-chain rings $R_{k,s}$
Fatmanur Gursoy, Elif Segah Oztas, Bahattin Yildiz · 2017-11-07 · via cs.IT updates on arXiv.org

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 $θ$ 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.

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