A Survey of Hadamard Difference Sets
نویسندگان
چکیده
difference set, Hadamard A (u,k,A) difference set is a k-element subset D of a group G of order u for which the multiset {dldl2: dl,d2 E D, dl =t= d2} contains each nonidentity element of G exactly A times. A Hadamard difference set (HDS) has parameters of the form (u,k, A) = (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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