This article is cited in 15 papers

RESEARCH ARTICLE

Semisimple group codes and dihedral codes

Flaviana S. Dutra^a, Raul A. Ferraz^b, C. Polcino Milies<sup>b

a</sup> Departamento de Matemática e Estatística (DME), Pontifícia Universidade Católica de Minas Gerais, Av. Dom José Gaspar, 500, Cep 30.535–901,Belo Horizonte, MG, Brazil
^b Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, Cep 05311–970, São Paulo, SP, Brazil

Abstract: We consider codes that are given as two-sided ideals in a semisimple finite group algebra ${\mathbb F}_qG$ defined by idempotents constructed from subgroups of $G$ in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two-sided ideals of ${\mathbb F}_qG$ in the case when $G$ is a dihedral group and extend these results also to a family of quaternion group codes. In the final section, we give a method of decoding; i.e., of finding and correcting eventual transmission errors.

Keywords: group code, minimal code, group algebra, idempotent, dihedral group, quaternion group.

MSC: 94B15, 94B60, 16S34, 20C05

Received: 20.08.2009
Revised: 24.09.2009

Language: English

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