Constructing permutation polynomials over finite fields

Authors

  • X. Qin
  • S. Hong Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, P.R. China

Keywords:

Permutation polynomial, linearized polynomial, linear translator, elementary symmetric polynomial

Abstract

In this paper, we construct several new permutation polynomials over finite fields. First, using the linearized polynomials, we construct the permutation polynomial of the form ki=1(Li(x)+γi)hi(B(x)) over Fqm, where Li(x) and B(x) are linearized polynomials. This extends a theorem of Coulter, Henderson and Matthews. Consequently, we generalise a result of Marcos by constructing permutation polynomials of the forms xh(λj(x)) and xh(μj(x)), where λj(x) is the j-th elementary symmetric polynomial of x,xq,...,xqm1 and μj(x)=TrFqm/Fq(xj). This answers an open problem raised by Zieve in 2010. Finally, by using the linear translator, we construct the permutation polynomial of the form L1(x)+L2(γ)h(f(x)) over Fqm, which extends the result of Kyureghyan. DOI: 10.1017/S0004972713000646

Author Biography

S. Hong, Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, P.R. China

Professor, Mathematics

Published

2014-03-25

Issue

Section

Articles