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Algebra and Discrete Mathematics, 2009, выпуск 3, страницы 28–48
(Mi adm131)
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Эта публикация цитируется в 15 научных статьях (всего в 15 статьях)
RESEARCH ARTICLE
Semisimple group codes and dihedral codes
Flaviana S. Dutraa, Raul A. Ferrazb, C. Polcino Miliesb a 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
Аннотация:
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.
Ключевые слова:
group code, minimal code, group algebra, idempotent, dihedral group, quaternion group.
Поступила в редакцию: 20.08.2009 Исправленный вариант: 24.09.2009
Образец цитирования:
Flaviana S. Dutra, Raul A. Ferraz, C. Polcino Milies, “Semisimple group codes and dihedral codes”, Algebra Discrete Math., 2009, no. 3, 28–48
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm131 https://www.mathnet.ru/rus/adm/y2009/i3/p28
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