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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2011.tde-10072011-093023
Document
Author
Full name
Rosemary Miguel Pires
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Grichkov, Alexandre (President)
Guerreiro, Marinês
Kornev, Alexandr
Guzzo Junior, Henrique
Zavarnitsine, Andrei
Title in Portuguese
Loops de código: automorfismos e representações
Keywords in Portuguese
automorfismos externos
códigos pares
loops de código
representações
vetores característivos
Abstract in Portuguese
Neste trabalho, estudamos Loops de Código. Para este estudo, introduzimos os loops de código a partir de códigos pares e depois, provamos que loops de código de posto $n$ podem ser caracterizados como imagem homomórfica de certos loops de Moufang livres com n geradores. Além disso, introduzimos o conceito de vetores característicos associados a um loop de código. Com os resultados da teoria estudada, classificamos todos os loops de código de posto 3 e 4, encontramos todos os grupos de automorfismos externos destes loops e, finalmente, determinamos todas as suas respectivas representações básicas.
Title in English
Code loops: automorphisms and representations
Keywords in English
characteristic vectors
code loops
even codes
outer automorphisms
representations
Abstract in English
This work is about code loops. For this study, we introduce the code loops from even codes and then we prove that code loops of rank n can be characterized as a homomorphic image of a certain free Moufang loops with $n$ generators. Moreover, we introduce the concept of characteristic vectors associated with code loops. With the results of this theory, we classify all the code loops of rank 3 and 4, we find all the groups of outer automorphisms of these loops and finally we determine all their basic representations.
 
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tese.pdf (529.10 Kbytes)
Publishing Date
2011-07-20
 
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