On Cyclic and Abelian Codes

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