  The problem of computing the dimension of a left/right ideal in a group
algebra F[G] of a finite group G over a field F is considered. The ideal
dimension is related to the rank of a matrix originating from a regular
left/right representation of G; in particular, when F[G] is semisimple, the
dimension of a principal ideal is equal to the rank of the matrix representing
a generator. From this observation, a bound and an efficient algorithm to
compute the dimension of an ideal in a group ring are established. Since group
codes are ideals in finite group rings, the algorithm allows efficient
computation of their dimension.
