Self-dual Repeated Root Cyclic and Negacyclic Codes over Finite Fields

In this paper we investigate repeated root cyclic and negacyclic codes of length p(r)m over F(p)s 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].