New cyclic difference sets with Singer parameters

Citations of this article
Mendeley users who have this article in their library.


The main result in this paper is a general construction of φ(m)/2 pairwise inequivalent cyclic difference sets with Singer parameters (v,k,λ)=(2m-1,2m-1,2m-2) for any m≥3. The construction was conjectured by the second author at Oberwolfach in 1998. We also give a complete proof of related conjectures made by No, Chung and Yun and by No, Golomb, Gong, Lee and Gaal which produce another difference set for each m≥7 not a multiple of 3. Our proofs exploit Fourier analysis on the additive group of GF(2m) and draw heavily on the theory of quadratic forms in characteristic 2. By-products of our results are a new class of bent functions and a new short proof of the exceptionality of the Müller-Cohen-Matthews polynomials. Furthermore, following the results of this paper, there are today no sporadic examples of difference sets with these parameters; i.e. every known such difference set belongs to a series given by a constructive theorem. © 2003 Elsevier Inc. All rights reserved.




Dillon, J. F., & Dobbertin, H. (2004). New cyclic difference sets with Singer parameters. Finite Fields and Their Applications, 10(3), 342–389.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free