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Designs, Codes and Cryptography

, Volume 87, Issue 4, pp 865–877 | Cite as

Relative blocking sets of unions of Baer subplanes

  • Aart Blokhuis
  • Leo StormeEmail author
  • Tamás Szőnyi
Article
  • 22 Downloads
Part of the following topical collections:
  1. Special Issue: Finite Geometries

Abstract

We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in \(\hbox {PG}(2,q^2)\) has size \(t(q+1)\) and consists of t Baer sublines, and, for large t, the smallest such set has size \(q^2+q+1\) and is itself a Baer subplane of \(\hbox {PG}(2,q^2)\). We also present a stability result in the first case.

Keywords

Blocking sets Baer subplanes Relative blocking sets Fractional cover Fractional covering number 

Mathematics Subject Classification

05B25 51E20 51E21 

Notes

Acknowledgements

The authors thank the referee for the many suggestions for improving the text of this article.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Ghent UniversityGhentBelgium
  3. 3.MTA-ELTE Geometric & Algebraic Combinatorics Research GroupELTE Eötvös Loránd UniversityBudapestHungary
  4. 4.UP FAMNITUniversity of PrimorskaKoperSlovenia

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