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A construction of small complete caps in projective spaces

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Abstract

In this work complete caps in PG(N, q) of size \({O(q^{\frac{N-1}{2}} \log^{300} q)}\) are obtained by probabilistic methods. This gives an upper bound asymptotically very close to the trivial lower bound \({\sqrt{2}q^{\frac{N-1}{2}}}\) and it improves the best known bound in the literature for small complete caps in projective spaces of any dimension. The result obtained in the paper also gives a new upper bound for l(m, 2, q)4, that is the minimal length n for which there exists an [n, n−m, 4] q 2 covering code with given m and q.

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Authors and Affiliations

  1. Department of Mathematics, Ghent University, Building S22, Krijgslaan 281, 9000, Ghent, Belgium

    Daniele Bartoli

  2. Department of Mathematics and Computer Sciences, Perugia University, Via Vanvitelli 1, 06123, Perugia, Italy

    Giorgio Faina, Stefano Marcugini & Fernanda Pambianco

Authors
  1. Daniele Bartoli
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  2. Giorgio Faina
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  3. Stefano Marcugini
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  4. Fernanda Pambianco
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Correspondence to Daniele Bartoli.

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Bartoli, D., Faina, G., Marcugini, S. et al. A construction of small complete caps in projective spaces. J. Geom. 108, 215–246 (2017). https://doi.org/10.1007/s00022-016-0335-1

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  • DOI: https://doi.org/10.1007/s00022-016-0335-1

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