Permutation polynomials on F_q induced from bijective Redei functions on subgroups of the multiplicative group of F_q

TL;DR

This paper constructs new permutation polynomials over finite fields using bijective Redei functions on specific subgroups, proving two conjectures about permutation trinomials.

Contribution

It introduces classes of permutation polynomials derived from Redei functions and confirms two recent conjectures in the field.

Findings

Constructed permutation polynomials over F_{Q^2}

Proved two conjectures on permutation trinomials

Established bijections on (Q+1)-th roots of unity

Abstract

We construct classes of permutation polynomials over F_{Q^2} by exhibiting classes of low-degree rational functions over F_{Q^2} which induce bijections on the set of (Q+1)-th roots of unity in F_{Q^2}. As a consequence, we prove two conjectures about permutation trinomials from a recent paper by Tu, Zeng, Hu and Li.