DNA Code Constructions from Some Codes over a Family of Finite Rings

Abstract

Firstly, by using a non-trivial automorphism θ_i over A_i, where i = 2, 3, ... , k, we define the skew cyclic codes over a family of the rings . By using them, we obtain the reversible DNA codes. In the second method, the necessary and sufficient condition of cyclic code over A_i to be reversible and reversible complement are given, where i = 2, 3, ... , k. By introducing a map, the DNA codes are obtained from them. In the third method, the special linear codes over  are established, where i = 2, 3, ... , k. By using them, the reversible and reversible complement DNA codes are obtained.