Several classes of permutation polynomials of the form [formula omitted] over [formula omitted

Abstract

In this paper, we give a further study on the permutation behavior of polynomials of a special form by considering the number of solutions of certain equations over finite fields. First, four classes of permutation polynomials of the form (x2m+x+δ)s+x over F22m are presented. Notably, some necessary and sufficient conditions for this kind of polynomials to permute F22m are provided. Second, we present several classes of permutation polynomials of the form (xpm−x+δ)s+x over Fp2m of odd characteristic, some of which can provide complete permutation polynomials of this form over F32m.