Códigos metacíclicos

• Autor(a) principal: Moreira, Poliana Luz
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://locus.ufv.br/handle/123456789/4902
• topic: Códigos; Grupos metacíclicos; Álgebras de grupo; Codes; Metacyclic groups; Group algebra; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

In this work, we study the eror-correction codes that are ideals in the group algebra FG(M;N;R) over a field F of characteristic 2, where the underlying group is a non-abelian metacyclic of odd order and has the following presentation: G(M;N;R) = ‹a, b : aM = bN = 1, ba = aRb›; onde mdc(M;R) = 1, RN = 1(mod M) e R ≠ 1. We use the theory of representations of the metacyclic groups to find the idempotent generators of the minimal central codes of FG(M;N;R) and prove that these codes are combinatorically equivalent to certain abelian codes whose minimum distances are not the best. However, some of these minimal central codes break down into direct sum of minimal left ideals (left codes), which have minimum distances greater than those abelian codes of comparable length and size. Thus, the study of certain metacyclic minimal (left) codes becomes more interesting. A detailed description of the theory of representations of metacyclic groups and some results on group algebras that support the determination of metacyclic codes are initially presented, as well as some results on cyclic codes.