G-equivalence in group algebras and minimal abelian codes
Information Theory
2012-03-27 v1 Group Theory
math.IT
Rings and Algebras
Abstract
Let G be a finite abelian group and F a field such that char(F) does not divide |G|. Denote by FG the group algebra of G over F. A (semisimple) abelian code is an ideal of FG. Two codes I and J of FG are G-equivalent if there exists an automorphism of G whose linear extension to FG maps I onto J In this paper we give a necessary and sufficient condition for minimal abelian codes to be G-equivalent and show how to correct some results in the literature.
Cite
@article{arxiv.1203.5742,
title = {G-equivalence in group algebras and minimal abelian codes},
author = {Raul Antonio Ferraz and Marinês Guerreiro and César Polcino Milies},
journal= {arXiv preprint arXiv:1203.5742},
year = {2012}
}
Comments
8 pages, 4 tables