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

Juli Loisiana Butar-Butar; Misa Br. Bukit

doi:10.34312/jjom.v4i2.13583

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

Juli Loisiana Butar-Butar, Misa Br. Bukit

Abstract

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.

Keywords

DNA Kode; Finite Field GF(4); Reversible Self-Dual Code

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DOI: https://doi.org/10.34312/jjom.v4i2.13583