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.

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doi.org/10.1016/j.ffa.2020.101664
Finite Fields and their Applications
School of Mathematics and Statistics

Reis, L. (Lucas), & Wang, Q. (2020). The dynamics of permutations on irreducible polynomials. Finite Fields and their Applications, 64. doi:10.1016/j.ffa.2020.101664