On cyclic DNA codes over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$

TL;DR

This paper explores the structure of cyclic DNA codes over a specific ring, focusing on codes satisfying reverse and reverse-complement constraints, which are relevant for DNA computing and error correction.

Contribution

It provides a detailed analysis of cyclic DNA codes over the ring un2+u2+u^22, including their structure and properties under reverse and reverse-complement constraints.

Findings

Characterization of cyclic DNA codes over the ring

Presentation of two code constructions satisfying constraints

Insights into code properties relevant for DNA computing

Abstract

In the present paper we study the structure of cyclic DNA codes of even lenght over the ring $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ where $u^3=0$. We investigate two presentations of cyclic codes of even lenght over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ satisfying the reverse constraint and reverse-complement constraint.