Permutation polynomials of the form (x(P)-x+delta)(S)+L(x)

Recently, several classes of permutation polynomials of the form (x(2) + x +delta)(s) + x over F-2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (x(P) - x + delta)(s) + L(x) over F-pm is investigated, where L(x) is a linearized polynomial with coefficients in F-p. Six classes of permutation polynomials on F-2m, are derived. Three classes of permutation polynomials over F-3m are also presented. (c) 2007 Elsevier Inc. All rights reserved