Abstract
We classify the smallest two fold blocking sets with respect to the (n−k)-spaces in PG(n, 2). We show that they either consist of two disjoint k-dimensional subspaces or are equal to a (k + 1)-dimensional space minus one point.
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Beutelspacher A.: Blocking sets and partial spreads in finite projective spaces. Geom. Dedicata 9, 130–157 (1980)
Bose R.C., Burton R.C.: A characterization of flat spaces in a finite geometry and the uniqueness of the Hamming and the McDonald codes. J. Comb. Theory 1, 96–104 (1966)
Govaerts P., Storme L.: The classification of the smallest nontrivial blocking sets of PG(n, 2). J. Comb. Theory A 113, 1543–1548 (2006)
Heim U.: Blockierende Mengen in endlichen projektiven Räumen. (German) [Blocking sets in finite projective spaces] Dissertation, Justus-Liebig-Universität Giessen, Giessen, 1995. Mitt. Math. Sem. Giessen 226, 82 (1996).
Helleseth T.: A characterization of codes meeting the Griesmer bound. Info. Control 50, 128–159 (1981)
Hirschfeld J.W.P.: Finite projective spaces of three dimensions. Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1985)
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Communicated by S. Ball.
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Aggarwal, M.L., Klein, A. & Storme, L. The characterisation of the smallest two fold blocking sets in PG(n, 2). Des. Codes Cryptogr. 63, 149–157 (2012). https://doi.org/10.1007/s10623-011-9541-x
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DOI: https://doi.org/10.1007/s10623-011-9541-x