Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group

Cerroni, Cinzia; Schulz, Ralph-Hardo

doi:10.1007/978-3-642-56755-1_9

Cited by 5 publications

(15 citation statements)

References 9 publications

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“…By using Spera's proposition, C. Cerroni and R.-H. Schulz constructed the following series of divisible designs [4]. Theorem 2.7 (Cerroni, Schulz) Let q = p n , where p is a prime, and let n, i ∈ N with i|n.…”

Section: Spera's Construction Principlementioning

confidence: 99%

“…Z consists of q + 1 lines (generators) each containing q points and intersecting the ideal plane in E. Each line contains precisely one parallel class of points. Now, keeping this in mind, we turn to Cerroni and Schulz's construction [4]. Consider a conic O in the ideal plane E ′ of the 3-dimensional affine space AG (3, q).…”

Section: Comparing Both Constructionsmentioning

confidence: 99%

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Some constructions of divisible designs from Laguerre geometries

Giese

Havlicek

Schulz

2005

Discrete Mathematics

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Section: Spera's Construction Principlementioning

confidence: 99%

Section: Comparing Both Constructionsmentioning

confidence: 99%

Some constructions of divisible designs from Laguerre geometries

Giese

Havlicek

Schulz

2005

Discrete Mathematics

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“…These DDs are finite analogues of tubular circle planes [23, p. 398]. We refer also to [7] (dual point of view) and [12] for the case when m = c = 1 and t = 3.…”

Section: Theorem 36 For Any Integer T ≥ 2 There Exist Infinitely Manmentioning

confidence: 99%

“…Ad (b): All orbits x G , where x ∈ X, have size q c according to (7). Ad (c): Let Y be a subset of X, such that Y is an R-transversal t-subset of X.…”

Section: Then For Each Non-negative Integermentioning

confidence: 99%

Lifting of divisible designs

2006

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The aim of this paper is to present a construction of t-divisible designs (DDs) for t > 3, because such DDs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties are employed. More precisely, in a first step an abstract construction, called t-lifting, is developed. It starts from a set X containing a t-DD and a group G acting on X. Then several explicit examples are given, where X is a subset of PG(n,q) and G is a subgroup of GL(n +1,q). In some cases X is obtained from a cone with a Veronesean or an h-sphere as its basis. In other examples, X arises from a projective embedding of a Witt design. As a result, for any integer t >= 2 infinitely many non-isomorphic t-DDs are found

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“…This method of Schulz and Spera, or slightly varied forms, are used, e.g., in [3][4][5][6]9,14,16]. In each of these constructions, a suitable subset P of affine hyperplanes is considered a point set and the point classes are induced by the parallelism relation given in the affine space.…”

Section: Definitions and Examplesmentioning

confidence: 99%