Several classes of permutation polynomials over the finite field [formula omitted]

Abstract

Let Fq denote the finite field with q elements. In this paper, based on the AGW criterion and determining the number of solutions to certain equations over the finite field Fp2m, several classes of permutation polynomials with given forms are proposed. Some of them are the permutation polynomials of the form (xpm−x+δ)s+L(x), where L(x) is a linearized polynomial. Others are the permutation polynomials of the form (xpm−x+δ)s1+(xpm−x+δ)s2+x.