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On multiple caps in finite projective spaces

Yves Edel (UGent) and Ivan Landjev
(2010) DESIGNS CODES AND CRYPTOGRAPHY. 56(2-3). p.163-175
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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.
Keywords
Multiple caps, Caps, Linear codes, Griesmer bound, Griesmer codes, Finite projective geometries, OPTIMAL LINEAR CODES, GALOIS SPACE, F5

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Citation

Please use this url to cite or link to this publication:

MLA
Edel, Yves, and Ivan Landjev. “On Multiple Caps in Finite Projective Spaces.” DESIGNS CODES AND CRYPTOGRAPHY, vol. 56, no. 2–3, 2010, pp. 163–75, doi:10.1007/s10623-010-9398-4.
APA
Edel, Y., & Landjev, I. (2010). On multiple caps in finite projective spaces. DESIGNS CODES AND CRYPTOGRAPHY, 56(2–3), 163–175. https://doi.org/10.1007/s10623-010-9398-4
Chicago author-date
Edel, Yves, and Ivan Landjev. 2010. “On Multiple Caps in Finite Projective Spaces.” DESIGNS CODES AND CRYPTOGRAPHY 56 (2–3): 163–75. https://doi.org/10.1007/s10623-010-9398-4.
Chicago author-date (all authors)
Edel, Yves, and Ivan Landjev. 2010. “On Multiple Caps in Finite Projective Spaces.” DESIGNS CODES AND CRYPTOGRAPHY 56 (2–3): 163–175. doi:10.1007/s10623-010-9398-4.
Vancouver
1.
Edel Y, Landjev I. On multiple caps in finite projective spaces. DESIGNS CODES AND CRYPTOGRAPHY. 2010;56(2–3):163–75.
IEEE
[1]
Y. Edel and I. Landjev, “On multiple caps in finite projective spaces,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 56, no. 2–3, pp. 163–175, 2010.
@article{939465,
  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.}},
  author       = {{Edel, Yves and Landjev, Ivan}},
  issn         = {{0925-1022}},
  journal      = {{DESIGNS CODES AND CRYPTOGRAPHY}},
  keywords     = {{Multiple caps,Caps,Linear codes,Griesmer bound,Griesmer codes,Finite projective geometries,OPTIMAL LINEAR CODES,GALOIS SPACE,F5}},
  language     = {{eng}},
  location     = {{Ghent, Belgium}},
  number       = {{2-3}},
  pages        = {{163--175}},
  title        = {{On multiple caps in finite projective spaces}},
  url          = {{http://doi.org/10.1007/s10623-010-9398-4}},
  volume       = {{56}},
  year         = {{2010}},
}

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