scholarly journals New results on covers and partial spreads of polar spaces

2005 ◽  
Vol 1 (1) ◽  
pp. 19-34 ◽  
Author(s):  
Andreas Klein ◽  
Klaus Metsch
Keyword(s):  
Polar Spaces ◽  
Partial Spreads

scholarly journals Partial ovoids and partial spreads in hermitian polar spaces

2007 ◽  
Vol 47 (1-3) ◽  
pp. 21-34 ◽  
Author(s):  
J. De Beule ◽  
A. Klein ◽  
K. Metsch ◽  
L. Storme
Keyword(s):  
Polar Spaces ◽  
Partial Spreads ◽  
Partial Ovoids

Small maximal partial spreads in classical finite polar spaces

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Andreas Klein ◽  
Klaus Metsch ◽  
Leo Storme
Keyword(s):  
Lower Bounds ◽  
Polar Spaces ◽  
Partial Spreads ◽  
Partial Ovoids

AbstractWe prove lower bounds on the size of small maximal partial spreads inQ+(4n+ 1,q),W(2n+ 1,q), andH(2n+ 1,q2). This research on the size of smallest maximal partial spreads in classical finite polar spaces is part of a detailed study on small and large maximal partial ovoids and spreads in classical finite polar spaces, performed in [De Beule, Klein, Metsch, Storme, Des. Codes Cryptogr 47: 21–34, 2008, De Beule, Klein, Metsch, Storme, European J. Combin 29: 1280–1297, 2008].

scholarly journals Maximal Partial Spreads of Polar Spaces

10.37236/5501 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Antonio Cossidente ◽  
Francesco Pavese
Keyword(s):  
Partial Spread ◽  
Polar Spaces ◽  
Partial Spreads ◽  
Maximal Partial Spread ◽  
Classical Polar Spaces

Some constructions of maximal partial spreads of finite classical polar spaces are provided. In particular we show that, for $n \ge 1$, $\mathcal{H}(4n-1,q^2)$ has a maximal partial spread of size $q^{2n}+1$, $\mathcal{H}(4n+1,q^2)$ has a maximal partial spread of size $q^{2n+1}+1$ and, for $n \ge 2$, $\mathcal{Q}^+(4n-1,q)$, $\mathcal{Q}(4n-2,q)$, $\mathcal{W}(4n-1,q)$, $q$ even, $\mathcal{W}(4n-3,q)$, $q$ even, have a maximal partial spread of size $q^n+1$.

scholarly journals Partial ovoids and partial spreads in symplectic and orthogonal polar spaces

2008 ◽  
Vol 29 (5) ◽  
pp. 1280-1297 ◽  
Author(s):  
J. De Beule ◽  
A. Klein ◽  
K. Metsch ◽  
L. Storme
Keyword(s):  
Polar Spaces ◽  
Partial Spreads ◽  
Partial Ovoids

On the embeddability of polar spaces

1992 ◽  
Vol 44 (3) ◽  
Author(s):  
Hans Cuypers ◽  
Peter Johnson ◽  
Antonio Pasini
Keyword(s):  
Polar Spaces

scholarly journals Minimal scattered sets and polarized embeddings of dual polar spaces

2007 ◽  
Vol 28 (7) ◽  
pp. 1890-1909 ◽  
Author(s):  
Bart De Bruyn ◽  
Antonio Pasini
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Opposite Relation on Dual Polar Spaces and Half-Spin Grassmann Spaces

2009 ◽  
Vol 54 (3-4) ◽  
pp. 301-308 ◽  
Author(s):  
Mariusz Kwiatkowski ◽  
Mark Pankov
Keyword(s):  
Polar Spaces ◽  
Dual Polar Spaces

scholarly journals Non-Classical Hyperplanes of Finite Thick Dual Polar Spaces

10.37236/7348 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Complete Classification ◽  
Polar Spaces ◽  
Dual Polar Spaces

We obtain a classification of the nonclassical hyperplanes of all finite thick dual polar spaces of rank at least 3 under the assumption that there are no ovoidal and semi-singular hex intersections. In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive. As a corollary, we also obtain a classification of the nonclassical hyperplanes of $DW(2n-1,q)$, $q$ even. In particular, we obtain a complete classification of all nonclassical hyperplanes of $DW(2n-1,q)$ if $q \in \{ 8,32 \}$.

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