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A Survey of Hadamard Difference Sets

Jedwab, Jonathan; Davis, James A.

HPL-94-14

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Abstract: A (v,k,L) difference set is a k-element subset D of a group G of order v for which multiset {d1d2-1:d1,d2 in D,d1 not equal to d2} contains each nonidentity element of G exactly L times. A Hadamard difference set (HDS) has parameters of the form (v,k,L) = (4N2, 2N2-N,N2-N). The Hadamard parameters provide the richest source of known examples of difference sets. The central question is: for each integer N, which groups of order 4N2 support a HDS? This question remains open, for abelian and nonabelian groups, despite an extensive literature. We survey the current state of knowledge of the subject.

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