On the Codes Over a Family of Rings and Their Applications to DNA Codes

Abstract

In this paper, the structures of the linear codes over a family of the rings [Formula In Abstract] are given, where [Formula In Abstract]. A map between the elements of the A<inf>t</inf> and the alphabet [Formula In Abstract] is constructed. The DNA codes are obtained with three different methods, by using the cyclic, skew cyclic codes over a family of the rings A<inf>t</inf> and θ<inf>i</inf>-set, where θ<inf>i</inf> is a non trivial automorphism on A<inf>i</inf>, for [Formula In Abstract]. © MSAEN.