On permutation binomials over finite fields

Authors

  • M. Ayad Universite du Littoral
  • K. Belghaba Universite d'Oran a Es Senia
  • O. Kihel Brock University

Keywords:

Finite fields, Permutation polynomials, Hermite-Dickson's Theorem

Abstract

Let Fq be the finite field of characteristic p containing q=pr elements and f(x)=axn+xm a binomial with coefficients in this field. If some conditions on the greatest common divisor of nm an q1 are satisfied then this polynomial does not permute the elements of the field. We prove in particular that if f(x)=axn+xm permutes Fp, where n>m>0 and aFp, then p1(d1)d, where d=gcd(nm,p1), and that this bound of p in term of d only, is sharp. We show as well how to obtain in certain cases a permutation binomial over a subfield of Fq from a permutation binomial over Fq. 10.1017/S0004972713000208

Author Biography

O. Kihel, Brock University

Associate Professor Department of Mathematics

Published

2013-12-02

Issue

Section

Articles