Some permutation polynomials via linear translators

Abstract

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from ${\mathbb{F}}_{q^n}$ to ${\mathbb{F}}_q$, many scholars constructed some classes of permutation polynomials. Motivated by previous works, we first naturally extend the notion of linear translators and then construct some permutation polynomials.

Finite field; permutation polynomial; linear translator; additive polynomial