The dynamics of permutations on irreducible polynomials

摘要

We study degree preserving maps over the set of irreducible polynomials over a finite field. In particular, we show that every permutation of the set of irreducible polynomials of degree k over F-q is induced by an action from a permutation polynomial of F(q)k with coefficients in F-q. The dynamics of these permutations of irreducible polynomials of degree k over F-q, such as fixed points and cycle lengths, are studied. As an application, we also generate irreducible polynomials of the same degree by an iterative method. (C) 2020 Elsevier Inc. All rights reserved.