Blocking sets of tangent lines to a hyperbolic quadric in PG(3,3)

被引：5
作者：
De Bruyn, Bart [1 ]
Sahoo, Binod Kumar [2 ]
Sahu, Bikramaditya [2 ]
机构：
[1] Univ Ghent, Dept Math Algebra & Geometry, Krijgslaan 281 S22, B-9000 Ghent, Belgium
[2] Natl Inst Sci Educ & Res, HBNI, Sch Math Sci, PO Jatni, Bhubaneswar 752050, Odisha, India
来源：
DISCRETE APPLIED MATHEMATICS | 2019年 / 266卷
关键词：
Projective space; Blocking set; Conic; Ovoid; Hyperbolic quadric;
D O I：
10.1016/j.dam.2018.12.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let Q(+)(3, q) be a hyperbolic quadric in PG(3, q) and T be the set of all lines of PG(3, q) which are tangent to Q(+)(3, q). If k is the minimum size of a T-blocking set in PG(3, q), then we prove that q(2) + 1 <= k <= q(2) + q. When q = 3, we show that: (i) there is no T-blocking set of size 10, and (ii) there are exactly two T-blocking sets of size 11 up to isomorphism. By means of the computer algebra systems GAP (The GAP Group, 2014) and Sage (Sage Mathematics Software (Version 6.3), 2014), we find that there exist no T-blocking sets of size q(2) + 1 for each odd prime power q <= 13. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：121 / 129
页数：9
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[21]   Minimal Blocking Sets in PG(2, 8) and Maximal Partial Spreads in PG(3, 8) [J].
J. Barát ;
A. Del Fra ;
S. Innamorati ;
L. Storme .
Designs, Codes and Cryptography, 2004, 31 :15-26
[22]   Blocking sets of nonsecant lines to a conic in PG(2,q), q odd [J].
Aguglia, A ;
Korchmáros, G .
JOURNAL OF COMBINATORIAL DESIGNS, 2005, 13 (04) :292-301
[23]   Blocking sets of tangent and external lines to a hyperbolic quadric in PG(3,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{PG(3,q)}$$\end{document}, q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{q}$$\end{document} even [J].
Binod Kumar Sahoo ;
Bikramaditya Sahu .
Proceedings - Mathematical Sciences, 2019, 129 (1)
[24]   Small minimal blocking sets and complete k-arcs in PG(2, p3) [J].
Polverino, O .
DISCRETE MATHEMATICS, 1999, 208 :469-476
[25]   Minimal blocking sets in PG(2,8) and maximal partial spreads in PGd(3,8) [J].
Barát, J ;
Del Fra, A ;
Innamorati, S ;
Storme, L .
DESIGNS CODES AND CRYPTOGRAPHY, 2004, 31 (01) :15-26
[26]   Orbits of Lines for a Twisted Cubic in PG(3, q) [J].
Davydov, Alexander A. ;
Marcugini, Stefano ;
Pambianco, Fernanda .
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (03)
[27]   On the blocking sets in S(3,6,22) and S(4,7,23) [J].
Bao, XM .
DISCRETE MATHEMATICS, 2000, 219 (1-3) :249-252
[28]   Two characterizations of the family of secant lines of an ovoid of PG(3, q) [J].
Napolitano, Vito .
JOURNAL OF GEOMETRY, 2019, 110 (02)
[29]   A characterization of the external lines of a hyperoval in PG(3, q), q even [J].
Zuanni, Fulvio .
DISCRETE MATHEMATICS, 2012, 312 (06) :1257-1259
[30]   On sets of type (m,h)(2) in PG (3,q) with m <= q [J].
Napolitano, Vito .
NOTE DI MATEMATICA, 2015, 35 (01) :109-123
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