用Dickson多项式构造差集(英文)

Constructing Cyclic Difference Sets by Using Dickson Polynomials

最近,Dillon和Dobbertin证明了在有限域F_q(q=2~m)的乘法群中,多项式(x+1)~d+x^d+1(其中d=2^(2k)-2~k+1)的像集是一个新的具有Singer参数的循环差集.利用有限域上的Fourier分析,本文证明了在有限域F_q(q=2~m)的乘法群中,一些用Dickson多项式构造的集合是具有Singer参数的循环差集.

Recently, J. F. Dillon, and H. Dobbertin proved that the image set of function △k （x） = （x ＋ 1）d＋ xd＋ 1 with d = 2^2k -2k＋ 1 is a new cyclic difference set in the additive group of the finite field F2m. Using Fourier analysis on the additive group, we prove that certain sets, constructed by using Dickson polynomials, form cyclic difference sets with Singer parameters.