Reversible and Reversible-Complement Double Cyclic Codes over F4+vF4 and its Application to DNA Codes

TL;DR

This paper investigates the algebraic structure of double cyclic codes over finite fields and rings, focusing on reversibility, reverse-complement constraints, and applications to DNA coding, including GC-content analysis.

Contribution

It provides necessary and sufficient conditions for reversibility of double cyclic codes over 4 and 4+v4, and establishes a correspondence between DNA double pairs and ring elements.

Findings

Characterization of reversible double cyclic codes over 4

Structure of codes over 4+v4 with reverse constraints

Mapping between DNA double pairs and ring elements

Abstract

In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we determine the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4+v\mathbb{F}_4$ with $v^2=v$, satisfying the reverse constraint and the reverse-complement constraint. Then we establish a one-to-one correspondence $\psi$ between the 16 DNA double pairs $S_{D_{16}} $ and the 16 elements of the finite ring $\mathbb{F}_4+v\mathbb{F}_4$. We also discuss the GC-content of DNA double cyclic codes.