A Survey of Hadamard Difference Sets

Authors

James A. Davis, University of RichmondFollow
Jonathan Jedwab

Abstract

A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d₁d₂^-1 : d1, d₂ ∈ D, d₁ ≠ d₂} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic according to the properties of the underlying group. Difference sets are important in design theory because they are equivalent to symmetric (v, k, λ) designs with a regular automorphism group [L].

Document Type

Book Chapter

Publication Date

1996

Publisher Statement

Copyright © 1996 Walter de Gruyter. This chapter first appeared in Groups, Difference Sets, and the Monster: Proceedings of a Special Research Quarter at the Ohio State University, Spring 1993.

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Recommended Citation

Davis, James A. and Jonathan Jedwab. "A Survey of Hadamard Difference Sets." In Groups, Difference Sets, and the Monster: Proceedings of a Special Research Quarter at the Ohio State University, Spring 1993, edited by K. T. Arasu, J. F. Dillon, K. Harada, S. Sehgal, and R. Solomon, 145-156. Ohio State University Mathematical Research Institute Publications. New York: Walter De Gruyter, 1996.