In 1987 Dillon and Schatz proved a theorem relating difference sets in elementary abelian 2-groups and designs with the symmetric difference property. As a corollary, they characterized designs with Hadamard parameters (where v=2^(2m)) whose codes have dimension 2m+2 and contain the all-1 vector, in terms of difference sets. Dillon, and later Assmus, asked whether the assumption on the all-1 vector could be removed. We show that the answer is yes.

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