Abstract
Nontrivial difference sets in 2-groups are part of the family of Hadamard difference sets. An abelian group of order 2^{2d+2} has a difference set if and only if the exponent of the group is less than or equal to 2^{d+2}. We provide an exponent bound for a more general type of 2-group which has a Hadamard difference set. A recent construction due to Davis and Iiams shows that we can attain this bound in at least half of the cases.
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