On minimal blocking sets of the generalized quadrangle $Q(4, q)$

Miroslava Cimráková,Veerle Fack

doi:10.46298/dmtcs.3466

Miroslava Cimráková, Veerle Fack

Open Access

https://doi.org/10.46298/dmtcs.3466

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Abstract

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 $q^2 + q$ (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 $q^2 + q - 2$ and we discuss their structure. By an exhaustive search we excluded the existence of a minimal blocking set of size $q^2 + 3$ in $Q(4,7)$.

Highlights

To cite this version: Miroslava Cimráková, Veerle Fack
The generalized quadrangle Q(4, q) arising from the parabolic quadric in P G(4, q) always has an ovoid. It is not known whether a minimal blocking set of size smaller than q2 + q exists in Q(4, q), q odd
For q = 5, 7, 9, 11 we found minimal blocking sets of size q2 + q − 2 and we discuss their structure

Summary

Introduction

To cite this version: Miroslava Cimráková, Veerle Fack. On minimal blocking sets of the generalized quadrangle Q(4, q). 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb ’05), 2005, Berlin, Germany. pp.299-302. hal-01184455. 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. For q = 5, 7, 9, 11 we found minimal blocking sets of size q2 + q − 2 and we discuss their structure.

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Conclusion