On Cyclic and Abelian Codes

In this paper, the minimum weight and the dimension of all cyclic codes of length pn over a field Fq, are computed, when p is an odd prime and Fq a finite field with q elements, assuming that Fq generates the group of invertible elements of Zpn. Furthermore, the minimum weight and dimension of codes which are sum of two minimal codes in Fq(Cp×Cp) are also computed. Finally, the efficiency of cyclic codes and noncyclic abelian codes of length p2 are compared.