In this paper, the minimum weight and the dimension of all cyclic codes of length $p^{n}$ over a field $\BBF_{q}$ , are computed, when $p$ is an odd prime and $\BBF_{q}$ a finite field with $q$ elements, assuming that $\overline{q}$ generates the group of invertible elements of $\BBZ_{p^{n}}$ . Furthermore, the minimum weight and dimension of codes which are sum of two minimal codes in $\BBF_{q}(C_{p}\times C_{p})$ are also computed. Finally, the efficiency of cyclic codes and noncyclic abelian codes of length $p^{2}$ are compared.