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Blocking sets of tangent and external lines to a hyperbolic quadric in \(\mathrm{PG}(3,q)\), \(q\) even. (English) Zbl 1405.05022

Summary: Let \(\mathcal {H}\) be a fixed hyperbolic quadric in the three-dimensional projective space \(\mathrm{PG}(3, q)\), where \(q\) is a power of 2. Let \(\mathbb {E}\) (respectively \(\mathbb {T}\)) denote the set of all lines of \(\mathrm{PG}(3, q)\) which are external (respectively tangent) to \(\mathcal {H}\). We characterize the minimum size blocking sets of \(\mathrm{PG}(3, q)\) with respect to each of the line sets \(\mathbb {T}\) and \(\mathbb {E}\cup \mathbb {T}\).

MSC:

05B25 Combinatorial aspects of finite geometries
51E21 Blocking sets, ovals, \(k\)-arcs
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