Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 997–1006 | Cite as

On m-ovoids of regular near polygons



We generalise the work of Segre (Ann Mat Pura Appl 4(70):1–201, 1965), Cameron et al. (J Algebra 55(2):257–280, 1978), and Vanhove (J Algebr Comb 34(3):357–373, 2011) by showing that nontrivial m-ovoids of the dual polar spaces \(\mathsf {DQ}(2d, q)\), \(\mathsf {DW}(2d-1,q)\) and \(\mathsf {DH}(2d-1,q^2)\) (\(d\geqslant 3\)) are hemisystems. We also provide a more general result that holds for regular near polygons.


Regular near polygon Dual polar space Hemisystem 

Mathematics Subject Classification

05B25 51E12 51E20 



The first author acknowledges the support of the Australian Research Council (ARC) Future Fellowship FT120100036. The second author acknowledges the support of an Australian Postgraduate Award and a UWA Top-Up Scholarship. The third author acknowledges the support of a Hackett Postgraduate Research Scholarship.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Centre for the Mathematics of Symmetry of Computation, School of Mathematics and StatisticsUniversity of Western AustraliaPerthAustralia
  2. 2.Department of MathematicsImperial CollegeLondonUK

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