DNA Code from Cyclic and Skew Cyclic Codes over F4[v]/⟨v3⟩

Abstract

The main motivation of this work is to study and obtain some reversible and DNA codes of length <i>n</i> with better parameters. Here, we first investigate the structure of cyclic and skew cyclic codes over the chain ring R:=F4[v]/⟨v3⟩. We show an association between the codons and the elements of R using a Gray map. Under this Gray map, we study reversible and DNA codes of length <i>n</i>. Finally, several new DNA codes are obtained that have improved parameters than previously known codes. We also determine the Hamming and the Edit distances of these codes.