Abstract
In this paper minimal m-blocking sets of cardinality at most \(\theta _m + \theta _{m - 1} \sqrt q \) in projective spaces PG(n,q) of square order q, q ≥ 16, are characterized to be (t, 2(m-t-1))-cones for some t with \(\max \{ - 1,2m - n - 1\} \leqslant t \leqslant m - 1\). In particular we will find the smallest m-blocking sets that generate the whole space PG(n,q) for 2m ≥ n ≥ m.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Beutelspacher, On baer subspaces of finite projective spaces, Math. Z., Vol. 184 (1983) pp. 301–319.
M. Bokler and K. Metsch, On the smallest minimal blocking sets in projective space generating the whole space, Contributions to Algebra and Geometry (to appear).
R. C. Bose and R. C. Burton, A characterization of flat spaces in a finite geometry and the uniqueness of the Hamming and the MacDonald codes, J. Comb. Theory, Vol. 1 (1966) pp. 96–104.
A. A. Bruen, Blocking sets in finite projective planes, SIAM. J. Appl. Math., Vol. 21 (1971) pp. 380–392.
A. A. Bruen, Blocking sets and skew subspaces of projective space, Canad. J. Math., Vol. 32 (1980) pp. 628–630.
U. Heim, Blockierende Mengen in endlichen projektiven Räumen, Mitt. Math. Semin. Giessen., Vol. 226 (1996) pp. 4–82.
M. Huber, Baer Cones in finite projective spaces, J. of Geom., Vol. 28 (1987) pp. 128–144.
K. Metsch and L. Storme, 2-Blocking sets in PG(n, q), q square, Contributions to Algebra and Geometry Vol. 41, No. 1 (2000) pp. 247–255.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bokler, M. Minimal Blocking Sets in Projective Spaces of Square Order. Designs, Codes and Cryptography 24, 131–144 (2001). https://doi.org/10.1023/A:1011236102371
Issue Date:
DOI: https://doi.org/10.1023/A:1011236102371