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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| 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 |
| 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. |
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