Factorization of a class of composed polynomials

2018/09/05 by Reis, Lucas
#11T30 #12E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.01762

Abstract

In this paper, we provide the degree distribution of irreducible factors of the composed polynomial f(L(x)) over \mathbb F_q, where f(x)∈ \mathbb F_q[x] is irreducible and L(x)∈ \mathbb F_q[x] is a linearized polynomial. We further provide some applications of our main result, including lower bounds for the number of irreducible factors of f(L(x)), constructions of high degree irreducible polynomials and the explicit factorization of f(x^q-x) under certain conditions on f(x).

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