The problem of computing the dimension of a left/right ideal in a group algebra  of a finite group  over a field  is considered. The ideal dimension is related to the rank of a matrix originating from a regular left/right representation of  in particular, when  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.

group algebra, ideal, group code, representation, rank, characteristic polynomial.