Permutation polynomials of the form (xpm−x+δ)s+L(x)(xpm−x+δ)s+L(x) over the finite field Fp2mFp2m of odd characteristic

In this paper, we propose several classes of permutation polynomials with the form (xpm−x+δ)s+L(x)(xpm−x+δ)s+L(x) over the finite field Fp2mFp2m, where p   is an odd prime, and L(x)L(x) is a linearized polynomial with coefficients in FpFp. The main method used in this paper is to determine the number of solutions of some equations over finite fields of odd characteristic.