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Designs, Codes and Cryptography

, Volume 44, Issue 1–3, pp 197–207 | Cite as

Characterization results on small blocking sets of the polar spaces Q +(2n + 1, 2) and Q +(2n + 1, 3)

  • J. De Beule
  • K. Metsch
  • L. Storme
Article
  • 45 Downloads

Abstract

In De Beule and Storme, Des Codes Cryptogr 39(3):323–333, De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q +(2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of Q +(7, 3). We continue this research by classifying all the minimal blocking sets of the hyperbolic quadrics Q +(2n + 1, 3), n ≥ 3, of size at most 3 n + 3 n–2. This means that the three smallest minimal blocking sets of Q +(2n + 1, 3), n ≥ 3, are now classified. We present similar results for q = 2 by classifying the minimal blocking sets of Q +(2n + 1, 2), n ≥ 3, of size at most 2 n + 2 n-2. This means that the two smallest minimal blocking sets of Q +(2n + 1, 2), n ≥ 3, are classified.

Keywords

Hyperbolic quadric Polar space Blocking set 

AMS Classifications

05B25 51D20 52C17 52C35 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Computer AlgebraGhent UniversityGhentBelgium
  2. 2.Mathematisches InstitutJustus-Liebig-Universität GießenGießenGermany

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