Permutation polynomials of finite fields of even characteristic from character sums

Abstract

In this paper, we investigate permutation polynomials over the finite field ${\mathbb{F}}_{q^n}$ with $q=2^m$, focusing on those in the form $\mathrm{Tr}(A{x}^{q+1})+L(x)$, where $A\in {\mathbb{F}}_{q^n}^{\ast }$ and $L$ is a $2$-linear polynomial over ${\mathbb{F}}_{q^n}$. By calculating certain character sums, we characterize these permutation polynomials and provide additional constructions.