Cyclic DNA codes over F2+uF2+vF2+uvF2

TL;DR

This paper explores the structure of cyclic DNA codes over a specific ring, establishing relations to simpler codes and analyzing constraints like reverse, reverse-complement, and GC content.

Contribution

It introduces a Gray map linking codes over a complex ring to simpler codes and studies cyclic DNA codes satisfying various biological constraints.

Findings

Established relations between codes over R and R1 using Gray map

Analyzed cyclic DNA codes satisfying reverse and reverse-complement constraints

Considered GC content constraint in code analysis

Abstract

In this work, we study the structure of cyclic DNA codes of arbitrary lengths over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2 by defining a Gray map between R and R1^2 where R1 is the ring with 4 elements. Cyclic codes of arbitrary lengths over R satisfied the reverse constraint and the reverse-complement constraint are studied in this paper. The GC content constraint is considered in the last.