Some permutation polynomials over finite fields

Abstract

Let p be prime, q = p m , and q − 1 = 7s. We completely describe the permutation behavior of the binomial P(x) = x r (1 + x es ) (1 ≤ e ≤ 6) over a finite field F q in terms of the sequence {a n } defined by the recurrence relation a n = a n−1 + 2a n−2 − a n−3 (n ≥ 3) with initial values a 0 = 3, a 1 = 1, and a 2 = 5.