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Complete Caps Projective Space Which are Disjoint from a Subspace of Codimension Two

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Book cover Finite Geometries

Part of the book series: Developments in Mathematics ((DEVM,volume 3))

Abstract

Working over the field of order 2 we consider those complete caps which are disjoint from some codimension 2 subspace of projective space. We derive restrictive conditions which such a cap must satisfy in order to be complete. Using these conditions we obtain explicit descriptions of complete caps which do not meet every hyperplane in at least 5 points. In particular, we determine the set of cardinalities of all such complete caps in all dimensions.

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References

  1. A.E. Brouwer, A.A. Bruen and D.L. Wehlau, There exist caps which block all subspaces of fixed codimension in PG(n, 2), J. Combin. Theory Ser. A 73(1996) 168–169.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Royal Military College, Kingston, Ontario, Canada, K7K 7B4

    David L. Wehlau

Authors
  1. David L. Wehlau
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Editor information

Editors and Affiliations

  1. University of Eindhoven, The Netherlands

    A. Blokhuis

  2. University of Sussex, England

    J. W. P. Hirschfeld

  3. University of Augsburg, Germany

    D. Jungnickel

  4. University of Ghent, Belgium

    J. A. Thas

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© 2001 Kluwer Academic Publishers

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Wehlau, D.L. (2001). Complete Caps Projective Space Which are Disjoint from a Subspace of Codimension Two. In: Blokhuis, A., Hirschfeld, J.W.P., Jungnickel, D., Thas, J.A. (eds) Finite Geometries. Developments in Mathematics, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0283-4_21

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  • DOI: https://doi.org/10.1007/978-1-4613-0283-4_21

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7977-5

  • Online ISBN: 978-1-4613-0283-4

  • eBook Packages: Springer Book Archive

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