Fatoração explícita de polinômios de Dickson sobre corpos finitos

Abstract

The objective of this work is to study the factorization in irreducible factors of (...) over (...), where q denotes the power of a prime p, (...) is a finite field with q elements and (...) is a Dickson polynomial of the first type of degree n in the indeterminate x and with parameter a. Imposing conditions on n and q we determine explicit expressions for the irreducible factors of this family of polynomials. We calculate the factorization by following the same techniques used in article [3], where are found explicitly the irreducible factors of the polynomial (...) over the field (...). This result generalizes the results find in [5],[7] e [12].