Semisimple group codes and dihedral codes

Abstract

We consider codes that are given as two-sided ideals in a semisimple finite group algebra FqG defined by idempotents constructed from subgroups of G in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two-sided ideals o f FqG in the case when G is a dihedral group and extend these results also to a family of quaternion group codes. In the final sectio n, we give a method of decoding; i.e., of finding and correcting eve ntual transmission errors.