Permutation Polynomials of Finite Fields of Even Characteristic From Character Sums

In this paper, we investigate permutation polynomials over a finite field Fqⁿ with q=2ᵐ, focusing on those in the form Tr(Axq+1)+L(x), where A∈ Fqⁿ^* and L is a $2$-linear polynomial over Fqⁿ. By calculating certain character sums, we characterize these permutation polynomials and provide additional constructions.