Construction of Cyclic Codes over $\mathbb{F}_2+u\mathbb{F}_2$ for DNA Computing

TL;DR

This paper develops cyclic codes over a specific ring for DNA computing, ensuring biological constraints are met, and introduces an infinite family of BCH DNA codes for improved applications.

Contribution

It introduces a novel construction of cyclic codes over 2+u2 for DNA computing, satisfying key biological constraints and extending to an infinite family of BCH DNA codes.

Findings

Codes satisfy reverse complement and GC content constraints

Codes avoid secondary structures

Infinite family of BCH DNA codes constructed

Abstract

We construct codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ with $u^2=0$. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint and avoid the secondary structure. they are derived from the cyclic complement reversible codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$. We also construct an infinite family of BCH DNA codes.