Construction of Cyclic DNA Codes Over the Ring Z4 + vZ4

Jie Liu,Hualu Liu

doi:10.1109/access.2020.3001283

Jie Liu, Hualu Liu

Open Access

https://doi.org/10.1109/access.2020.3001283

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Abstract

In this work, we investigate DNA codes of odd length over the finite ring R = Z 4 +vZ 4 , v 2 = v. Firstly, we give a map Φ from R n to {A, T, G, C} 2n . Then cyclic codes of odd length satisfying the reverse and reverse-complement constraint are characterized over such ring. Moreover, when C is a reverse-complement cyclic code over R, we prove that Φ(C) is a cyclic DNA code by using the method different from all the previously known ones, which helps us finding a new DNA code with 256 codewords. Finally, we consider the GC content of code C over finite ring Z 4 + vZ 4 by means of the Gray images of the minimal generating set of C.

Highlights

Deoxyribonucleic acid (DNA) contains the instructions for the structure and function of cells
When C is a cyclic code over R, we prove that (C) is a reverse-complement DNA code by using the method different from that in [2], [23]
(1) (C) gives a reversible cyclic DNA code of length 2n, size K, with minimum distance code at least d over the alphabet {A, T, G, C}; (2) if r(x) = 1+x +x2+. . .+xn−1 belongs to C, (C) gives a cyclic DNA code of length 2n, size K, with minimum distance code at least d over the alphabet {A, T, G, C}

Summary

INTRODUCTION

Deoxyribonucleic acid (DNA) contains the instructions for the structure and function of cells. They in [6] studied the structure of cyclic DNA codes of odd length over the finite ring F2 + uF2 + vF2 + uvF2 + v2F2 + uv2F2, u2 = 0, v3 = v, which plays an important role in genetics, bioengineering and DNA computing. Inspired by these works, in this paper, we study DNA codes over the finite ring of 16 elements, namely, R = Z4 + vZ4, v2 = v.

PRELIMINARIES

DNA CODES OVER THE RING R

THE GC WEIGHT

EXAMPLES IN CONSTRUCTING DNA CODES

CONCLUSION