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A construction of small complete caps in projective spaces

(2017) JOURNAL OF GEOMETRY. 108(1). p.215-246
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Organization
Abstract
In this work complete caps in PG(N, q) of size O(q(N-1/2) log(300) q) are obtained by probabilistic methods. This gives an upper bound asymptotically very close to the trivial lower bound root 2q(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.
Keywords
Complete caps, projective spaces, quasi-perfect codes, covering codes, COVERING RADIUS, COMPLETE ARCS, LINEAR CODES, Q EVEN, PG(N, Q), PLANES, Q)

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Citation

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

MLA
Bartoli, Daniele et al. “A Construction of Small Complete Caps in Projective Spaces.” JOURNAL OF GEOMETRY 108.1 (2017): 215–246. Print.
APA
Bartoli, D., Faina, G., Marcugini, S., & Pambianco, F. (2017). A construction of small complete caps in projective spaces. JOURNAL OF GEOMETRY, 108(1), 215–246.
Chicago author-date
Bartoli, Daniele, Giorgio Faina, Stefano Marcugini, and Fernanda Pambianco. 2017. “A Construction of Small Complete Caps in Projective Spaces.” Journal of Geometry 108 (1): 215–246.
Chicago author-date (all authors)
Bartoli, Daniele, Giorgio Faina, Stefano Marcugini, and Fernanda Pambianco. 2017. “A Construction of Small Complete Caps in Projective Spaces.” Journal of Geometry 108 (1): 215–246.
Vancouver
1.
Bartoli D, Faina G, Marcugini S, Pambianco F. A construction of small complete caps in projective spaces. JOURNAL OF GEOMETRY. 2017;108(1):215–46.
IEEE
[1]
D. Bartoli, G. Faina, S. Marcugini, and F. Pambianco, “A construction of small complete caps in projective spaces,” JOURNAL OF GEOMETRY, vol. 108, no. 1, pp. 215–246, 2017.
@article{8573531,
  abstract     = {In this work complete caps in PG(N, q) of size O(q(N-1/2) log(300) q) are obtained by probabilistic methods. This gives an upper bound asymptotically very close to the trivial lower bound root 2q(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.},
  author       = {Bartoli, Daniele and Faina, Giorgio and Marcugini, Stefano and Pambianco, Fernanda},
  issn         = {0047-2468},
  journal      = {JOURNAL OF GEOMETRY},
  keywords     = {Complete caps,projective spaces,quasi-perfect codes,covering codes,COVERING RADIUS,COMPLETE ARCS,LINEAR CODES,Q EVEN,PG(N,Q),PLANES,Q)},
  language     = {eng},
  number       = {1},
  pages        = {215--246},
  title        = {A construction of small complete caps in projective spaces},
  url          = {http://dx.doi.org/10.1007/s00022-016-0335-1},
  volume       = {108},
  year         = {2017},
}

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