Constructing Cyclic Difference Sets by Using Dickson Polynomials
Xiwang Cao · Advances in Mathematics · 2009
Recently,J.F.Dillon,and H.Dobbertin proved that the image set of functionΔ_k(x)=(x+1)~d+ x~d+1 with d=2~(2k)-2~k+1 is a new cyclic difference set in the additive group of the finite field F_(2~m).Using Fourier analysis on the additive group,we prove that certain sets, constructed by using Dickson polynomials,form cyclic difference sets with Singer parameters.