On some permutation polynomials over finite fields

Abstract

Let p be prime, q = pm, and q - 1 = 7s. We completely describe the permutation behavior of the binomial P(x) = xr (1 + xes) (1 ≤ e ≤ 6) over a finite field Fq in terms of the sequence {an} defined by the recurrence relation an = an-1 + 2an-2 - an-3 (n ≥ 3) with initial values a0 = 3, a1, = 1, and a2 = 5. Copyright © 2005 Hindawi Publishing Corporation.