Self-dual repeated root cyclic and negacyclic codes over finite fields

摘要

In this paper we investigate repeated root cyclic and negacyclic codes of length p^r m over Fps with (m, p) = 1. In the case p odd, we give necessary and sufficient conditions on the existence of negacyclic self-dual codes. When m = 2m^'' with m^'' odd, we characterize the codes in terms of their generator polynomials. This provides simple conditions on the existence of self-dual negacyclic codes, and generalizes the results of Dinh [6]. We also answer an open problem concerning the number of self-dual cyclic codes given by Jia et al. [11].