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A Note on Difference Sets

✍ Scribed by Hikoe Enomoto; Mariko Hagita; Makoto Matsumoto

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 234 KB
Volume: 84
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1998.2881

No coin nor oath required. For personal study only.

✦ Synopsis

Let D be a (v, k, *)-difference set in a group G. Assume that G has a normal subgroup N such that GÂN is cyclic or nearly cyclic. Under the self-conjugacy assumption on exp(GÂN), we shall give bounds on |N| and *. The theorem is applicable to a wider variety of parameters for groups, not necessarily abelian. These bounds exclude a (96, 20, 4)-difference set in ZÂ4Z_ZÂ8Z_ZÂ3Z or ZÂ2Z_ZÂ2Z_ZÂ8Z_ ZÂ3Z, which were recently proved by

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