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Doctoral Thesis
DOI
Document
Author
Full name
Fernanda Diniz de Melo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Milies, Francisco Cesar Polcino (President)
Brusamarello, Rosali
Chalom, Alegria Gladys
Ferraz, Raul Antonio
Guerreiro, Marinês
Title in Portuguese
Sobre códigos cíclicos e abelianos
Keywords in Portuguese
Anéis de grupo
Código abeliano
Código cíclico
Peso de códigos lineares
Abstract in Portuguese
Neste trabalho calculamos o peso e a dimensão de todos os códigos cíclicos de comprimento pn na álgebra de grupo FqCpn, onde p é um número primo e Fq é um corpo finito de característica q. Também calculamos o peso do código dado pela soma de dois códigos abelianos minimais em Fq(Cp × Cp), dessa forma foi possível fazer uma breve comparação entre códigos cíclicos e abelianos não cíclicos de comprimento p2.
Title in English
On cyclic codes and abelian codes
Keywords in English
Abelian code
Cyclic code
Group ring
Weight linear code
Abstract in English
In this work we compute the weight and the dimension of all cyclic codes of length pn in the group algebra FqCpn, where p is a prime number and Fq is a finite field of characteristic q. Furthermore, we compute the weight of codes which are given by the sum of two minimal abelian codes in Fq(Cp × Cp). In this way, it was possible to compare briefly cyclic codes and non-cyclic abelian codes of length p2.
 
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Publishing Date
2019-09-25
 
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