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Non-splitting Abelian (4 t, 2, 4 t, 2 t) Relative Difference Sets and Hadamard Cocycles

✍ Scribed by G. Hughes

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 144 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0349

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✦ Synopsis

Using cohomology we show that in studying the existence of an abelian non-splitting (4t, 2, 4t, 2t) relative difference set, D, we can assume the groups in question have a certain simple form. We obtain an explicit constructive equivalence between generalized perfect binary arrays and cocycles that define Hadamard matrices and thereby show directly that the existence of D corresponds to that of a symmetric Hadamard matrix of a certain form. This extends the well-known equivalence in the case of splitting relative difference sets.

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