Polinômios de permutação e q-polinômios

In this work, we discuss some results involving permutation polynomials and q-polynomials, both defined over finite fields. Firstly we introduce basic concepts and theorems concerning each one of those polynomials classes. Then, we find criteria to determinate if a given q-polynomial is a permutatio...

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Detalhes bibliográficos
Autor: Sousa, João Paulo Guardieiro
Formato: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2021
País:Brasil
Recursos:Universidade Federal de Uberlândia (UFU)
Repositorio:Repositório Institucional da UFU
Idioma:portugués
OAI Identifier:oai:repositorio.ufu.br:123456789/31369
Acesso em linha:https://repositorio.ufu.br/handle/123456789/31369
https://doi.org/10.14393/ufu.di.2021.55
Access Level:acceso abierto
Palavra-chave:Corpos finitos
Finite fields
Polinômios de permutação
Permutation polynomials
q-polinômios
q-polynomials
Polinômios planares
Planar polynomials
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Polinômios
Descrição
Resumo:In this work, we discuss some results involving permutation polynomials and q-polynomials, both defined over finite fields. Firstly we introduce basic concepts and theorems concerning each one of those polynomials classes. Then, we find criteria to determinate if a given q-polynomial is a permutation one and study two methods in order to obtain q-polynomials which already have this property. At the end of this dissertation, we will apply the results obtained previously in order to find conditions under which a specific polynomial class can be planar.