On Skew Cyclic Codes over a Mixed Alphabet and Their Applications to DNA Codes

Abstract

In this paper, we introduce skew cyclic codes over the mixed alphabet F4R, where F-4 is the finite field with 4 elements and R = F-4 + uF(4) + vF(4), u(2) = u , v(2) = v , uv = vu = 0. Our results include a description of the generator polynomials of such codes and a necessary and sufficient condition for an F4R-skew cyclic code to be reversible complement.