Abstract
Short description of the Lunelli–Sce hyperoval and its automorphism group is given.
Similar content being viewed by others
References
Abdukhalikov, K.: Bent functions and line ovals. Finite Fields Appl. 47, 94–124 (2017)
Abdukhalikov, K.: Hyperovals and bent functions. Eur. J. Combin. 79, 123–139 (2019)
Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: the user language. J. Symb. Comput. 24(3/4), 235–265 (1997)
Brown, J.M.N., Cherowitzo, W.: The Lunelli–Sce hyperoval in PG(2,16). J. Geom. 69(1–2), 15–36 (2000)
Cherowitzo, W.: Hyperoval webpage. http://math.ucdenver.edu/~wcherowi/research/hyperoval/hypero.html. Accessed 26 Oct 2019
Cherowitzo, W.: Hyperovals in Desarguesian planes of even order. Ann. Discrete Math. 37, 87–94 (1988)
Cherowitzo, W.: Hyperovals in Desarguesian planes: an update. Discrete Math. 155, 31–38 (1996)
Cherowitzo, W., Penttila, T., Pinneri, I., Royle, G.F.: Flocks and ovals. Geom. Dedicata 60, 17–37 (1996)
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)
Dembowski, P.: Finite Geometries. Springer, Berlin (1968)
Fisher, J.C., Schmidt, B.: Finite Fourier series and ovals in PG \((2,2^{h})\). J. Aust. Math. Soc. 81(1), 21–34 (2006)
Hall Jr., M.: Ovals in the Desarguesian plane of order 16. Ann. Mat. Pura Appl. 4(102), 159–176 (1975)
Hirschfeld, J.W.P.: Projective Geometries Over Finite Fields. Oxford Mathematical Monographs, 2nd edn. The Clarendon Press, Oxford University Press, New York (1998)
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)
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)
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)
O’Keefe, C.M., Penttila, T.: Hyperovals in PG(2,16). Eur. J. Comb. 12(1), 51–59 (1991)
Payne, S.E., Conklin, J.E.: An unusual generalized quadrangle of order sixteen. J. Combin. Theory Ser. A 24(1), 50–74 (1978)
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
Corresponding author
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
About this article
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
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s00022-019-0509-8