Some Construction of Group Divisible Designs With Singer Groups

Document Type

Article

Publication Date

12-10-1991

Abstract

Let D be a Menon difference set in a group G with parameters (4u2, 2u2 - u, u2 - u) and T a divisible difference set (DDS) with parameters (m, n, k, λ1, λ2) in a group H relative to a subgroup N satisfying what we call property (M): mn = 4(k - λ2). We provide a recursive construction and show that E = (D, T) ∪ (G\D, H\T) is a DDS in G ⊕ H relative to N. Furthermore, E also satisfies property (M). Our proof shows that this construction will work only when T has property (M). We also provide several series of examples of DDS's admitting -1 as a multiplier. We characterize the DDS's with λ1 = 0 and (M). Finally we give a geometric construction of an infinite family of symmetric divisible designs admitting a Singer group.

DOI

10.1016/0012-365X(91)90419-3

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