Some classes of complete permutation polynomials in the form of (x^pm − x + δ ) ^s + ax^pm + bx over F _{p 2m}

Abstract

Several classes of complete permutation polynomials (CPPs) in the form of (x p m − x + δ) s + ax p m + bx over F p 2m are described in this paper. For fractional exponent s, the permutation properties of the given polynomials are proved by the AGW criterion and for determining the bijectivity of the corresponding piecewise functions. For exponent s satisfying s = i(p m − 1) + p j , the main proofs here depend on the AGW criterion and the quantity of solutions for certain linearised equations. Several results generalise some earlier results on permutation polynomials (PPs).