DNA codes over two noncommutative rings of order four

TL;DR

This paper introduces a novel class of DNA codes constructed over two specific noncommutative rings of order four, leveraging quasi self-duality to meet biological constraints.

Contribution

It presents the first construction of DNA codes over noncommutative rings of order four using quasi self-dual codes, addressing biological constraints.

Findings

Codes satisfy fixed GC-content constraints

Codes meet reverse-complement minimum distance requirements

Framework applicable to biological DNA coding constraints

Abstract

In this paper, we describe a new type of DNA codes over two noncommutative rings $E$ and $F$ of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over $E$ and $F$. Using quasi self-duality, we can describe fixed GC-content constraint weight distributions and reverse-complement constraint minimum distributions of those codes.