DNA Code from Cyclic and Skew Cyclic Codes over <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><mn>4</mn></msub><mrow><mo>[</mo><mi>v</mi><mo>]</mo></mrow><mo>/</mo><mrow><mo>〈</mo><msup><mi>v</mi><mn>3</mn></msup><mo>〉</mo></mrow></mrow></semantics></math></inline-formula>

Abstract

The main motivation of this work is to study and obtain some reversible and DNA codes of length n 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 n. 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.

Keywords

• reversible code
• gray map
• DNA codes