International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2631-2640
doi:10.1155/IJMMS.2005.2631

On some permutation polynomials over finite fields

Amir Akbary1 and Qiang Wang2

1Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive West, AB, Lethbridge T1K 3M4, Canada
2School of Mathematics and Statistics, Carleton University, ON, Ottawa K1S 5B6, Canada

Received 8 March 2005; Revised 5 May 2005

Copyright © 2005 Amir Akbary and Qiang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.