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A small minimal blocking set in PG(n, p (t) ), spanning a (t-1)-space, is linear

(2013) DESIGNS CODES AND CRYPTOGRAPHY. 68(1-3). p.25-32
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Abstract
In this paper, we show that a small minimal blocking set with exponent e in PG(n, p (t) ), p prime, spanning a (t/e - 1)-dimensional space, is an -linear set, provided that p > 5(t/e)-11. As a corollary, we get that all small minimal blocking sets in PG(n, p (t) ), p prime, p > 5t - 11, spanning a (t - 1)-dimensional space, are -linear, hence confirming the linearity conjecture for blocking sets in this particular case.
Keywords
Blocking set, Linearity conjecture, Linear set, NUMBER, SPACES, FINITE-FIELD, Q)

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Citation

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

MLA
Sziklai, Peter, and Geertrui Van de Voorde. “A Small Minimal Blocking Set in PG(n, p (t) ), Spanning a (t-1)-space, Is Linear.” DESIGNS CODES AND CRYPTOGRAPHY 68.1-3 (2013): 25–32. Print.
APA
Sziklai, P., & Van de Voorde, G. (2013). A small minimal blocking set in PG(n, p (t) ), spanning a (t-1)-space, is linear. DESIGNS CODES AND CRYPTOGRAPHY, 68(1-3), 25–32.
Chicago author-date
Sziklai, Peter, and Geertrui Van de Voorde. 2013. “A Small Minimal Blocking Set in PG(n, p (t) ), Spanning a (t-1)-space, Is Linear.” Designs Codes and Cryptography 68 (1-3): 25–32.
Chicago author-date (all authors)
Sziklai, Peter, and Geertrui Van de Voorde. 2013. “A Small Minimal Blocking Set in PG(n, p (t) ), Spanning a (t-1)-space, Is Linear.” Designs Codes and Cryptography 68 (1-3): 25–32.
Vancouver
1.
Sziklai P, Van de Voorde G. A small minimal blocking set in PG(n, p (t) ), spanning a (t-1)-space, is linear. DESIGNS CODES AND CRYPTOGRAPHY. 2013;68(1-3):25–32.
IEEE
[1]
P. Sziklai and G. Van de Voorde, “A small minimal blocking set in PG(n, p (t) ), spanning a (t-1)-space, is linear,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 68, no. 1–3, pp. 25–32, 2013.
@article{5807939,
  abstract     = {{In this paper, we show that a small minimal blocking set with exponent e in PG(n, p (t) ), p prime, spanning a (t/e - 1)-dimensional space, is an -linear set, provided that p > 5(t/e)-11. As a corollary, we get that all small minimal blocking sets in PG(n, p (t) ), p prime, p > 5t - 11, spanning a (t - 1)-dimensional space, are -linear, hence confirming the linearity conjecture for blocking sets in this particular case.}},
  author       = {{Sziklai, Peter and Van de Voorde, Geertrui}},
  issn         = {{0925-1022}},
  journal      = {{DESIGNS CODES AND CRYPTOGRAPHY}},
  keywords     = {{Blocking set,Linearity conjecture,Linear set,NUMBER,SPACES,FINITE-FIELD,Q)}},
  language     = {{eng}},
  number       = {{1-3}},
  pages        = {{25--32}},
  title        = {{A small minimal blocking set in PG(n, p (t) ), spanning a (t-1)-space, is linear}},
  url          = {{http://dx.doi.org/10.1007/s10623-012-9751-x}},
  volume       = {{68}},
  year         = {{2013}},
}

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