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On hyperovals of polar spaces

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Abstract

We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon \({\mathbb E_3}\) has up to isomorphism a unique full embedding into the dual polar space DH(5, 4).

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Authors and Affiliations

  1. Department of Mathematics, Ghent University, Krijgslaan 281 (S22), 9000, Gent, Belgium

    Bart De Bruyn

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  1. Bart De Bruyn
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Correspondence to Bart De Bruyn.

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Communicated by Leo Storme.

Dedicated to the memory of András Gács (1969–2009).

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De Bruyn, B. On hyperovals of polar spaces. Des. Codes Cryptogr. 56, 183–195 (2010). https://doi.org/10.1007/s10623-010-9400-1

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  • DOI: https://doi.org/10.1007/s10623-010-9400-1

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