Reversible DNA codes over a family of non-chain rings

In this work we extend results introduced in [15]. Especially, we solve the reversibility problem for DNA codes over the non chain ring $R_{k,s}=F_{4^{2k}}[u_1,\ldots,u_{s}]/\langle u_1^2-u_1,\ldots, u_s^2-u_s\rangle$. We define an automorphism $\theta$ 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.Comment: 10 page

Metode Reversible Self-Dual untuk Konstruksi Kode DNA atas Lapangan Hingga GF(4)

The DNA molecule chain consists of two complementary strands composed of a sequence of four nucleotide bases, namely adenine (A), cytosine (C), guanine (G) and thymine (T). DNA code is a set of codewords with a fixed length of the alphabet {A, C, T, G}. DNA coding is one application of coding theory over a finite field. The set {A, C, T, G} is identified as finite field GF(4) = {0, 1, w, w2} with w2 + w + 1 = 0. The reversible self-dual (RSD) code over the finite field GF(4) is a code whose dual is itself and the reverse of each codeword contained in the code. This study aims to obtain an algorithm to construct a DNA code derived from the RSD C code on the field to GF(4) which is called the Reversible Self-Dual Method. The aspects studied include the characteristics that form the basis properties of the theory in compiling the DNA code algorithm over the RSD code over GF(4). The compiled algorithm is a DNA code construction method of codeword length even that conforms to the Hamming distance constraint, reverse-complement constraint, and GC-content constraint. The input of the algorithm is a generator matrix of RSD code C with a minimum distance of d and the output is a DNA code that satisfies these three constraints