Almost difference sets and reversible divisible difference sets
type: Item
instance of: scholarly article
title: Almost difference sets and reversible divisible difference sets
zbMATH Open document ID: 0794.05008
DOI: 10.1007/BF01194853
author: James A. Davis
published in: Archiv der Mathematik
publication date: 1994-08-16T00:00:00Z
review text: Almost difference sets are divisible difference sets with the property that \(\lambda_ 1\) and \(\lambda_ 2\) differ by 1 (they would be difference sets if \(\lambda_ 1=\lambda_ 2\)). Two constructions are given. The first set of parameters are \((4,3^{2a},2(3^{2a}-3^ a),3^{2a}- 2\cdot 3^ a,3^{2a}-2\cdot 3^ a+ 1)\), and these are similar to \((4\cdot 3^{2a},2\cdot 3^{2a}- 3^ a,3^{2a}-3^ a)\) (Menon) difference sets. The second construction is built by using the hyperplanes of EA\((q^{d+1})\) together with a \((m,n,h,h-1,\lambda_ 2)\) divisible difference set to get a \((m,nq^{d+1},q^ d h,q^ d\Bigl({q^ d-1\over q-1}\Bigr),q^{d-1}\lambda_ 2) \text{DDS}\). This is not an almost difference set in general, but we note two special cases where it is an almost difference set. We give two modifications of this basic construction, and we also give examples where this construction is reversible.
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 572365
zbMATH Keywords: divisible difference sets
zbMATH Keywords: almost difference set
zbMATH Keywords: reversible
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01194853
OpenAlex ID: W2042816375
description: scientific article; zbMATH DE number 572365