Inequivalence of difference sets: on a remark of Baumert

Catháin, Padraig Ó (2013) Inequivalence of difference sets: on a remark of Baumert. Electronic Journal of Combinatorics, 20 1: 38.1-38.19.

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Author Catháin, Padraig Ó
Title Inequivalence of difference sets: on a remark of Baumert
Journal name Electronic Journal of Combinatorics   Check publisher's open access policy
ISSN 1077-8926
Publication date 2013-02
Sub-type Article (original research)
Open Access Status File (Publisher version)
Volume 20
Issue 1
Start page 38.1
End page 38.19
Total pages 19
Place of publication United States
Publisher Electronic Journal of Combinatorics
Collection year 2014
Language eng
Formatted abstract
An often cited statement of Baumert in his book Cyclic difference sets asserts that four well known families of cyclic (4t−1,2t−1,t−1) difference sets are inequivalent, apart from a small number of exceptions with t≤8. We are not aware of a proof of this statement in the literature.

Three of the families discussed by Baumert have analogous constructions in non-cyclic groups. We extend his inequivalence statement to a general inequivalence result, for which we provide a complete and self-contained proof. We preface our proof with a survey of the four families of difference sets, since there seems to be some confusion in the literature between the cyclic and non-cyclic cases.
Keyword Matrices
Difference sets
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2014 Collection
 
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