Reversible DNA codes over a family of non-chain rings R_k,s

2017/11/07 by Gursoy, Fatmanur, Oztas, Elif Segah, Yildiz, Bahattin
#92D20 #94B05 #94B15 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1711.02385

Abstract

In this paper, we solve the reversibility problem for DNA codes over the non-chain ring R_k,s=\mathbbF_4^2k[u₁,...,u_s]/< u₁²-u₁,..., u_s²-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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