Lucas Reis

Elements of high order in Artin-Schreier extensions of finite fields F q

In this paper, we find a lower bound for the order of the coset x + b in the Artin-Schreier extension F q x / ( x p - x - a ) , where b ź F q satisfies a generic special condition.

Factoring polynomials of the form f(xn)∈Fq[x]

Abstract Let f ( x ) ∈ F q [ x ] be an irreducible polynomial of degree m and exponent e. For each positive integer n, such that ν p ( q − 1 ) ≥ ν p ( e ) + ν p ( n ) for all prime divisors p of n, we show a fast algorithm to determine the irreducible factors of f ( x n ) . Using this algorithm, we give the complete factorization of x n − 1 into irreducible factors in the case where n = d p t , p is an odd prime, q is a generator of the group Z p 2 ⁎ and either d = 2 m with m ≤ ν 2 ( q − 1 ) or d = r a , where r is a prime dividing q − 1 but not p − 1 .

Nilpotent linearized polynomials over finite fields and applications

Let

The functional graph of linear maps over finite fields and applications

q

On the multiplicative order of the roots of bXqr+1−aXqr+dX−c

be a prime power and

The action of GL2(Fq) on irreducible polynomials over Fq, revisited

\mathbb F_{q^n}

Existence results on k-normal elements over finite fields.

be the finite field with

The dynamics of permutations on irreducible polynomials.

q^n

On the factorization of iterated polynomials

elements, where

Factorization of a class of composed polynomials

n>1