#### 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*, *λ _{1}*,

*λ*

_{2}) divisible difference set (DDS) provided that the differences

*dd*for

^{'-1}*d*,

*d'*∈

*D*,

*d ≠ d'*contain every nonidentity element of

*N*exactly

*λ*times and every element of

_{1}*G - N*exactly

*λ*

_{2}times. Difference sets are used to generate designs, as described by [4] and [9]. D will be called an Almost Difference set (ADS) if

*λ*and

_{1}*λ*

_{2}differ by 1. The reason why these are interesting involves their relationship to symmetric difference sets. A symmetric difference set is a DDS with

*λ*=

_{1}*λ*

_{2}, 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.