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.