Conical embeddings of Steiner systems
type: Item
instance of: scholarly article
title: Conical embeddings of Steiner systems
zbMATH Open document ID: 0653.51006
DOI: 10.1007/BF02844701
author: Dieter Jungnickel
author: Scott A. Vanstone
publication date: 1987-01-01T00:00:00Z
review text: The classical Steiner system \(S(3,2^ a+1;2^{ab}+1)\) is also known as inversive space. A construction of \(S(3,2^ a+1;2^{ab}+1)\) uses an ovoid in \(PG(3,2^ a)\) the blocks being determined by intersections of the ovoid with planes. While this provides an embedding into space, in this paper the authors give a natural embedding into a plane \(PG(2,2^{ab})\) of such Steiner systems. More precisely, they use a conic of \(PG(2,2^{ab})\) as the point set of \(S(3,2^ a+1;2^{ab}+1);\) the blocks will be determined by the intersection with certain subplanes of order \(2^ a\). Consequently, every such Steiner system is naturally embedded into PG(2,K) where K is the algebraic closure of GF(2).
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51E25
zbMATH DE Number: 4065800
zbMATH Keywords: Steiner system
zbMATH Keywords: inversive space
zbMATH Keywords: embedding
reviewed by: Giorgio Faina
MaRDI profile type: Publication
cites work: Q3851217
cites work: On the geometry of planar difference sets
cites work: Historical notes on Steiner systems
published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 4065800