A Family of Cyclic Difference Sets with Singer Parameters

Abstract

Very recently, J.F.Dillon, and H.Dobbertin proved that, the image set of function ∆ k (x) = (x + 1) d + x d + 1, (where d = 2 2k − 2 k + 1), is a new cyclic difference set in the additive group of the finite field GF (2 m). Using Fourier analysis on the additive group, we prove that certain sets, constructed by using Dickson polynomials, form a new cyclic difference sets with Singer parameters.

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