Permutation Polynomials of Finite Fields of Even Characteristic From Character Sums

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