Specific permutation polynomials over finite fields

Abstract

We present new classes of permutation polynomials over finite fields. If q is the order of the finite field, some of these polynomials have the form x r f ( x ( q − 1 ) / d ) , where d | ( q − 1 ) . We also present some permutation polynomials involving the trace function, which plays an additive role analogous to x ( q − 1 ) / d . Finally, we present a generalization involving other symmetric functions of x , x p , … , x q / p .