Journal of Geometry

, Volume 108, Issue 1, pp 75–98 | Cite as

On dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\)

  • Anton Betten
  • Ulrich Dempwolff
  • Alfred Wassermann
Article
  • 62 Downloads

Abstract

We discuss dual hyperovals of rank 4 over \({{\mathbb{F}}_2}\). In particular, we classify all such dual hyperovals if the ambient space has dimension 7 or 8. We also determine the bilinear dual hyperovals in the case of an ambient space of dimension 9 or 10. A classification of all dual hyperovals in dimension 9 seems possible in the near future.

Keywords

Dual hyperoval enumeration finite projective geometry 

Mathematics Subject Classification

51E21 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Anton Betten
    • 1
  • Ulrich Dempwolff
    • 2
  • Alfred Wassermann
    • 3
  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA
  2. 2.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  3. 3.Department of MathematicsUniversity of BayreuthBayreuthGermany

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