Designs, Codes and Cryptography

, Volume 72, Issue 1, pp 119–128 | Cite as

Some large partial ovoids of \(Q^-(5,q)\), for odd \(q\)



We give explicit descriptions of some of the largest partial ovoids of \(Q^-(5,q)\) currently known (for \(q\) odd). Apart from two generic constructions, the other (sporadic) examples are for fields of order \(q \le 11\). As far as we know, most of these results are new. Others were found earlier by computer but have never been described explicitly. All our constructions are formulated using elliptic quadratic forms that are not in standard form.


Partial ovoid Elliptic quadric Generalized quadrangle 

Mathematics Subject Classification

05B25 51D20 51E12 51E20 



I would like to thank Jan De Beule en Klaus Metsch for many valuable discussions and for introducing me to this subject. I would also like to thank the anonymous referees for many useful comments and suggestions.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceGhent UniversityGentBelgium

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