On the Skew Cyclic Codes and the Reversibility Problem for DNA 4-Bases

Abstract

The DNA 4-bases are matched with the 256 elements of the finite ring $$R=F_{4}+uF_{4}+vF_{4}+uvF_{4}$$, where $$ u^{2}=u,v^{2}=v,uv=vu$$. By defining a non trivial automorphism over R, the skew cyclic codes over the finite ring R are introduced. The reversible DNA codes are obtained, by using the skew cyclic codes whose generator polynomials satisfy some conditions. Thanks to this, the reversibility problem for DNA 4-bases can be solved. Moreover, the Gray images of the skew cyclic codes over the finite ring are determined.