Skip to main content
Log in

Short description of the Lunelli–Sce hyperoval and its automorphism group

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

Short description of the Lunelli–Sce hyperoval and its automorphism group is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abdukhalikov, K.: Bent functions and line ovals. Finite Fields Appl. 47, 94–124 (2017)

    Article  MathSciNet  Google Scholar 

  2. Abdukhalikov, K.: Hyperovals and bent functions. Eur. J. Combin. 79, 123–139 (2019)

    Article  MathSciNet  Google Scholar 

  3. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: the user language. J. Symb. Comput. 24(3/4), 235–265 (1997)

    Article  MathSciNet  Google Scholar 

  4. Brown, J.M.N., Cherowitzo, W.: The Lunelli–Sce hyperoval in PG(2,16). J. Geom. 69(1–2), 15–36 (2000)

    Article  MathSciNet  Google Scholar 

  5. Cherowitzo, W.: Hyperoval webpage. http://math.ucdenver.edu/~wcherowi/research/hyperoval/hypero.html. Accessed 26 Oct 2019

  6. Cherowitzo, W.: Hyperovals in Desarguesian planes of even order. Ann. Discrete Math. 37, 87–94 (1988)

    Article  MathSciNet  Google Scholar 

  7. Cherowitzo, W.: Hyperovals in Desarguesian planes: an update. Discrete Math. 155, 31–38 (1996)

    Article  MathSciNet  Google Scholar 

  8. Cherowitzo, W., Penttila, T., Pinneri, I., Royle, G.F.: Flocks and ovals. Geom. Dedicata 60, 17–37 (1996)

    Article  MathSciNet  Google Scholar 

  9. Cherowitzo, W.E., O’Keefe, C.M., Penttila, T.: A unified construction of finite geometries associated with q-clans in characteristic 2. Adv. Geom. 3(1), 1–21 (2003)

    Article  MathSciNet  Google Scholar 

  10. Dembowski, P.: Finite Geometries. Springer, Berlin (1968)

    Book  Google Scholar 

  11. Fisher, J.C., Schmidt, B.: Finite Fourier series and ovals in PG \((2,2^{h})\). J. Aust. Math. Soc. 81(1), 21–34 (2006)

    Article  MathSciNet  Google Scholar 

  12. Hall Jr., M.: Ovals in the Desarguesian plane of order 16. Ann. Mat. Pura Appl. 4(102), 159–176 (1975)

    Article  MathSciNet  Google Scholar 

  13. Hirschfeld, J.W.P.: Projective Geometries Over Finite Fields. Oxford Mathematical Monographs, 2nd edn. The Clarendon Press, Oxford University Press, New York (1998)

    Google Scholar 

  14. Korchmáros, G.: Collineation groups transitive on the points of an oval[ \((q+2)\)-arc] of \(S_{2, q}\)for q even. Atti Sem. Mat. Fis. Univ. Modena 27(1), 89–105 (1979)

  15. Korchmáros, G.: Old and new results on ovals in finite projective planes. In: Keedwell, A. (ed.) Surveys in Combinatorics, 1991 (Guildford, 1991). London Mathematical Society Lecture Note Series, vol. 166, pp. 41–72. Cambridge University Press, Cambridge (1991)

    Google Scholar 

  16. Lunelli, L., Sce, M.: k-archi completi nei piani proiettivi desarguesiani di rango 8 e 16, p. 15. Centro di Calcoli Numerici, Politecnico di Milano, Milan (1958) (in Italian)

  17. O’Keefe, C.M., Penttila, T.: Hyperovals in PG(2,16). Eur. J. Comb. 12(1), 51–59 (1991)

    Article  MathSciNet  Google Scholar 

  18. Payne, S.E., Conklin, J.E.: An unusual generalized quadrangle of order sixteen. J. Combin. Theory Ser. A 24(1), 50–74 (1978)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The author would like to thank the anonymous referee for his suggestions that greatly improved this article. This work was supported by Grant 31S366.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kanat Abdukhalikov.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdukhalikov, K. Short description of the Lunelli–Sce hyperoval and its automorphism group. J. Geom. 110, 54 (2019). https://doi.org/10.1007/s00022-019-0509-8

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1007/s00022-019-0509-8

Keywords

Mathematics Subject Classification

Navigation