Factorization of composed polynomials and applications

Autor(es)

Brochero-Martinez, F. E. ^[1] ; Reis, Lucas ^[2] ; Silva-Jesus, Lays ^{[1, 3]}

Afiliação do(s) autor(es)

^[1] Univ Fed Minas Gerais, Dept Matemat, BR-30123970 Belo Horizonte, MG - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Fed Roraima, Dept Matemat, BR-69310000 Boa Vista, RR - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE MATHEMATICS; v. 342, n. 12 DEC 2019.
• Citações Web of Science: 0

Resumo

Let F-q be the finite field with q elements, where q is a prime power and let n be a positive integer. In this paper, we explore the factorization of f(x(n)) over F-q, where f(x) is an irreducible polynomial over F-q. Our main results provide generalizations of recent works on the factorization of binomials x(n) - 1. As an application, we provide an explicit formula for the number of irreducible factors of f(x(n)) under some generic conditions on f and n. (C) 2019 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 18/03038-2 - Mapas polinomiais em corpos finitos e suas aplicações
• Beneficiário: Lucas da Silva Reis
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado