Abstract
An x-tight set of a hyperbolic quadric Q +(2n + 1, q) can be described as a set M of points with the property that the number of points of M in the tangent hyperplanes of points of M is as big as possible. We show that such a set is necessarily the union of x mutually disjoint generators provided that x ≤ q and n ≤ 3, or that x < q, n ≥ 4 and q ≥ 71. This unifies and generalizes many results on x-tight sets that are presently known, see (J Comb Theory Ser A 114(7):1293–1314 [1], J Comb Des 16(4):342–349 [5], Des Codes Cryptogr 50:187–201 [4], Adv Geom 4(3):279–286 [8], Bull Lond Math Soc 42(6):991–996 [11]).
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.
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Beukemann, L., Metsch, K. Small tight sets of hyperbolic quadrics. Des. Codes Cryptogr. 68, 11–24 (2013). https://doi.org/10.1007/s10623-012-9676-4
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DOI: https://doi.org/10.1007/s10623-012-9676-4