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Small Blocking Sets in Higher Dimensions

✍ Scribed by Tamás Szőnyi; Zsuzsa Weiner

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 133 KB
Volume: 95
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3152

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✦ Synopsis

We show that small blocking sets in PG(n, q) with respect to hyperplanes intersect every hyperplane in 1 modulo p points, where q= p h . The result is then extended to blocking sets with respect to k-dimensional subspaces and, at least when p>2, to intersections with arbitrary subspaces not just hyperplanes. This can also be used to characterize certain non-degenerate blocking sets in higher dimensions. Furthermore we determine the possible sizes of small minimal blocking sets with respect to k-dimensional subspaces.

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