2014/03/31 by Elia, Michele, Gorla, Elisa
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1403.7920
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.