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Proper blocking sets in projective spaces

✍ Scribed by Udo Heim

Book ID: 104113799
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 477 KB
Volume: 174
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00294-4

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✦ Synopsis

In this paper we introduce the new concept of proper blocking sets B infinite projective spaces, that means every hyperplane contains a point of B, no line is contained in B, and there is no hyperplane that induces a blocking set. In Theorem 1.4, we prove that a blocking set in PG(d, q), q ~> 3, that has less than the number of points of a blocking set in PG(2, q) of minimum cardinality plus one, already contains a blocking set in a plane and is therefore not proper. In the last section, we construct various examples of proper blocking sets with a small number of points.

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