Further results on permutation polynomials of the form (xpm−x+δ)s+L(x) over Fp2m

In this paper, some classes of permutation polynomials of the form (xpm−x+δ)s+L(x) over the finite field Fp2m are investigated by determining the number of solutions of certain equations, where L(x)=x or xpm+x. More precisely, for an integer s satisfying s(pm+1)≡pm+1 (mod p2m−1), we give four classes of permutation polynomials of the form (x2m+x+δ)s+x over F22m, and five classes of permutation polynomials of the form (x3m−x+δ)s+x3m+x over F32m, respectively.