The structure of group rings provides an efficient setting for compact storage of error-correcting codes and for developing fast encoding and decoding algorithms. It is well known that all classical codes can be regarded as ideals in several classes of group rings. The reader may consult, for example, [7], [15], [16], [18], [19], [20], [22], [24], etc. In this paper, we shall consider abelian codes in the semisimple case,

survey some known results, and show how to determine all minimal abelian codes, their dimensions, and weights in an interesting situation: when the number of simple components of the group algebra is minimal. In the last section we consider similar results in the case of finite dihedral groups.