DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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On minimal blocking sets of the generalized quadrangle

Miroslava Cimráková, Veerle Fack


The generalized quadrangle Q(4,q) arising from the parabolic quadric in PG(4,q) always has an ovoid. It is not known whether a minimal blocking set of size smaller than q2 + q (which is not an ovoid) exists in Q(4,q),  q odd. We present results on smallest blocking sets in Q(4,q),  q odd, obtained by a computer search. For q = 5,7,9,11 we found minimal blocking sets of size q2 + q - 2 and we discuss their structure. By an exhaustive search we excluded the existence of a minimal blocking set of size q2 + 3 in Q(4,7).

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