On some bounds on the minimum distance of cyclic codes over finite fields

Recently, A. Zeh, A. Wachter-Zeh, M. Gadouleau and S. Bezzateev gave a method to obtain new lower bounds on the minimum distance of cyclic codes over finite fields. Here we present some results on a generalization of this method. Then we apply it to several examples of cyclic codes and compare some known bounds with the bounds obtained by this generalization.