  Several relations and bounds for the dimension of principal ideals in group
algebras are determined by analyzing minimal polynomials of regular
representations. These results are used in the two last sections. First, in the
context of semisimple group algebras, to compute, for any abelian code, an
element with Hamming weight equal to its dimension. Finally, to get bounds on
the minimum distance of certain MDS group codes. A relation between a class of
group codes and MDS codes is presented. Examples illustrating the main results
are provided.
