Blocking Sets in Desarguesian Affine and Projective Planes

Research output: Contribution to journalArticle

74 Citations (Scopus)

Abstract

In this paper we show that blocking sets of cardinality less than 3(q+ 1)/2 (q=pn) in Desarguesian projective planes intersect every line in 1 moduloppoints. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous results of Rédei, which were proved for a special class of blocking sets. In the particular caseq=p2, the above result implies that a nontrivial blocking set either contains a Baer-subplane or has size at least 3(q+ 1)/2; and this result is sharp. As a by-product, new proofs are given for the Jamison, Brouwer-Schrijver theorem on blocking sets in Desarguesian affine planes, and for Blokhuis' theorem on blocking sets in Desarguesian projective planes.

Original languageEnglish
Pages (from-to)187-202
Number of pages16
JournalFinite Fields and Their Applications
Volume3
Issue number3
DOIs
Publication statusPublished - Jul 1997

Fingerprint

Blocking Set
Affine plane
Projective plane
Byproducts
Cardinality
Brouwer's theorem
Short Intervals
Intersect
Imply
Line
Theorem

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Blocking Sets in Desarguesian Affine and Projective Planes. / Szőnyi, T.

In: Finite Fields and Their Applications, Vol. 3, No. 3, 07.1997, p. 187-202.

Research output: Contribution to journalArticle

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