Reversible (bisymmetric) self-dual codes over finite fields with characteristic two and their applications to DNA codes

Abstract

Some recent studies reveal the development of reversible (bisymmetric) self-dual codes over fields of order 2 and 4. In this paper, we give new methods of constructing reversible (bisymmetric) self-dual codes over finite fields with characteristic two. This approach is motivated by the well-known reversible (bisymmetric) self-dual codes over finite fields of order two. We first investigated some properties of a reversible (bisymmetric) self-dual code over finite fields with characteristic two. Next, we developed a method to construct a new reversible (bisymmetric) self-dual code over finite fields with characteristic two. Additionally, we found an optimal reversible (bisymmetric) self-dual code over finite fields with characteristic two, and this method is applied to construct DNA codes.