Permutation polynomials of the form s(xp−x+δ)+L(x)

Recently, several classes of permutation polynomials of the form s(x2+x+δ)+x over Fm2 have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form s(xp−x+δ)+L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on Fm2 are derived. Three classes of permutation polynomials over Fm3 are also presented.