On DNA Codes using the Ring Z4 + wZ4

TL;DR

This paper explores DNA code construction using the algebraic structure of the ring Z4 + wZ4, establishing a correspondence with DNA codewords and creating new classes that satisfy biological constraints, some of which are optimal.

Contribution

It introduces a novel algebraic approach to DNA code design using the ring Z4 + wZ4 and defines a distance-preserving map to generate codes meeting biological constraints.

Findings

Several new classes of DNA codes satisfying reverse and reverse complement constraints.

Some constructed DNA codes are proven to be optimal.

The method provides a systematic algebraic framework for DNA code construction.

Abstract

In this work, we study the DNA codes from the ring R = Z4 + wZ4, where w^2 = 2+2w with 16 elements. We establish a one to one correspondence between the elements of the ring R and all the DNA codewords of length 2 by defining a distance-preserving Gau map phi. Using this map, we give several new classes of the DNA codes which satisfies reverse and reverse complement constraints. Some of the constructed DNA codes are optimal.