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A Nonexistence Result For Abelian Menon Difference Sets Using Perfect Binary Arrays, K. T. Arasu, James A. Davis, Jonathan Jedwab
A Nonexistence Result For Abelian Menon Difference Sets Using Perfect Binary Arrays, K. T. Arasu, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A Menon difference set has the parameters (4N2, 2N2-N, N2-N). In the abelian case it is equivalent to a perfect binary array, which is a multi-dimensional matrix with elements ±1 such that all out-of-phase periodic autocorrelation coefficients are zero. Suppose that the abelian group H×K×Zpα contains a Menon difference set, where p is an odd prime, |K|=pα, and pj≡−1 (mod exp (H)) for some j. Using the viewpoint of perfect binary arrays we prove that K must be cyclic. A …
Research Announcement: Recursive Construction For Families Of Difference Sets, James A. Davis, Jonathan Jedwab
Research Announcement: Recursive Construction For Families Of Difference Sets, James A. Davis, Jonathan Jedwab
Department of Math & Statistics Faculty Publications
A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1, d2, ∈ D} contains each nonzero element of G exactly λ times; n = k-λ.