Abstract
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 Fq is induced by an action from a permutation polynomial of Fqk with coefficients in Fq. The dynamics of these permutations of irreducible polynomials of degree k over Fq, 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have