Almost Difference Sets and Reversible Divisible Difference Sets

Authors

James A. Davis, University of RichmondFollow

DOI

10.1007/BF01194853

Abstract

Let G be a group of order mn and N a subgroup of G of order n. If D is a k-subset of G, then D is called a (m, n, k, λ₁, λ₂) divisible difference set (DDS) provided that the differences dd^'-1 for d, d' ∈ D, d ≠ d' contain every nonidentity element of N exactly λ₁ times and every element of G - N exactly λ₂ times. Difference sets are used to generate designs, as described by [4] and [9]. D will be called an Almost Difference set (ADS) if λ₁ and λ₂ differ by 1. The reason why these are interesting involves their relationship to symmetric difference sets. A symmetric difference set is a DDS with λ₁ = λ₂, so the ADS are "almost" difference sets. Symmetric difference sets are becoming more and more difficult to construct, and this is as close as we can get with a divisible difference set.

Document Type

Article

Publication Date

12-1992

Publisher Statement

Copyright © 1992, Birkhäuser-Verlag. This article first appeared in Archiv der Mathematik: 59:6 (1992), 595-602.

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Recommended Citation

Davis, James A. "Almost Difference Sets and Reversible Divisible Difference Sets." Archiv Der Mathematik 59, no. 6 (December 1992): 595-602. doi: 10.1007/BF01194853.