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On multiple caps in finite projective spaces

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Abstract

In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the size of such caps. Furthermore, we generalize two product constructions for (k, 2)-caps to caps with larger n. We give explicit constructions for good caps with small n. In particular, we determine the largest size of a (k, 3)-cap in PG(3, 5), which turns out to be 44. The results on caps in PG(3, 5) provide a solution to four of the eight open instances of the main coding theory problem for q = 5 and k = 4.

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Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Ghent, Belgium

    Yves Edel

  2. New Bulgarian University, 21 Montevideo Str., 1618, Sofia, Bulgaria

    Ivan Landjev

  3. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev, 1113, Sofia, Bulgaria

    Ivan Landjev

Authors
  1. Yves Edel
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  2. Ivan Landjev
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Correspondence to Ivan Landjev.

Additional information

Communicated by L. Storme.

Dedicated to the memory of András Gács (1969–2009).

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Edel, Y., Landjev, I. On multiple caps in finite projective spaces. Des. Codes Cryptogr. 56, 163–175 (2010). https://doi.org/10.1007/s10623-010-9398-4

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  • DOI: https://doi.org/10.1007/s10623-010-9398-4

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