Computing the dimension of ideals in group algebras, with an application to coding theory
Information Theory
2019-09-09 v2 math.IT
Rings and Algebras
Abstract
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.
Cite
@article{arxiv.1403.7920,
title = {Computing the dimension of ideals in group algebras, with an application to coding theory},
author = {Michele Elia and Elisa Gorla},
journal= {arXiv preprint arXiv:1403.7920},
year = {2019}
}
Comments
13 pages, submitted