On the dimension of ideals in group algebras, and group codes
Information Theory
2020-07-24 v2 math.IT
Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.2002.06407,
title = {On the dimension of ideals in group algebras, and group codes},
author = {Elias Javier Garcia Claro and Horacio Tapia Recillas},
journal= {arXiv preprint arXiv:2002.06407},
year = {2020}
}