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In this paper, we provide a construction of (q+1)-ovoids of the hyperbolic quadric Q+(7,q), q an odd prime power, by glueing (q+1)/2-ovoids of the elliptic quadric Q(5,q). This is possible by controlling some intersection properties of (putative) m-ovoids of elliptic quadrics. It eventually yields (q+1)-ovoids of Q+(7,q) not coming from a 1-system. Secondly, for certain values of q, we construct line spreads of PG(3,q) that have as many secants to a given elliptic quadric as possible. This is then used to construct m-ovoids for m∈{2,4,6,8,10} in Q+(7,3).

Originele taal-2English
Aantal pagina's15
TijdschriftFinite Fields and Their Applications
StatusPublished - mrt 2024

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© 2024 Elsevier Inc.


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