An explicit expression for Euclidean self-dual cyclic codes over F<inf>2^m</inf>+uF<inf>2^m</inf> of length 2^s

Abstract

Let F2m be the finite field of 2m elements and s be any positive integer. The existing literature only gives an effective calculation method to represent all distinct Euclidean self-dual cyclic codes of length 2s over the finite chain ring F2m+uF2m(u2=0), such as in Cao et al., (2019). As a development of this topic, we provide an explicit expression for each of these self-dual cyclic codes, using binomial coefficients. The Gray image of any self-dual cyclic code over F2m+uF2m of length 2s is a self-dual 2-quasi-cyclic code over F2m of length 2s+1. In particular, we give a generator matrix for each of these self-dual 2-quasi-cyclic codes over F2m.