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A Bose-Burton type theorem for quadrics

✍ Scribed by Klaus Metsch

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 224 KB
Volume: 11
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10051

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✦ Synopsis

Abstract

Let Q be a non‐degenerate quadric defined by a quadratic form in the finite projective space PG(d,q). Let r be the dimension of the generators of Q. For all k with 2 ≤ k < r we determine the smallest cardinality of a set B of points with the property that every subspace of dimension k that is contained in Q meets B. It turns out that the smallest examples consist of the non‐singular points of quadrics S ∩ Q for suitable subspaces S of codimension k of PG(d,q). For k = 1, the same result was known before. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 317–338, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10051

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