On Double Cyclic Codes and Applications to DNA Codes

In this paper, we investigate the structure of double cyclic codes of length (α,β) over R=F4+ϱF4,ϱ2=0 and give a minimal spanning set of double cyclic codes. Moreover, we extend this study to construct DNA codes from R-double cyclic codes. Furthermore, we explore reversible and reversible-complement double cyclic codes over R and present a necessary and sufficient condition for separable R-double cyclic codes to be reversible and reversible-complement R-double cyclic codes. Also, we study reversible and reversible-complement double cyclic codes over R for non-separable case and construct some optimal R-double cyclic codes, and several DNA codes to support our results.