Tightening Turyn's bound for Hadamard difference sets

Authors:
Omar A. Abughneim;Ken W. Smith
Affiliations:
Department of Mathematics, Faculty of Science, Jordan University, Amman, Jordan 11942;Department of Mathematics, Central Michigan University, Mount Pleasant, USA 48859
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2008

Citing 4
Cited 0

Design theory

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Non-Abelian Hadamard difference sets

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On difference sets in groups of order 4p2

Journal of Combinatorial Theory Series A
A survey of Hadamard difference sets

GDSTM '93 Proceedings of a special research quarter on Groups, difference sets, and the monster

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Abstract

This work examines the existence of (4q 2,2q 2驴q,q 2驴q) difference sets, for q=p f , where p is a prime and f is a positive integer. Suppose that G is a group of order 4q 2 which has a normal subgroup K of order q such that G/K 驴 C q 脳C 2脳C 2, where C q ,C 2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does not admit (4q 2,2q 2驴q,q 2驴q) difference sets.