Abstract
Two new infinite families of hyperovals on the generalized quadrangle \(\mathcal H (3,q^2), q\) odd, are constructed.
Similar content being viewed by others
References
Buekenhout F., Hubaut X.: Locally polar spaces and related rank 3 groups. J. Algebra 45, 391–434 (1977).
Cameron P.J., Hughes D.R., Pasini A.: Extended generalized quadrangles. Geom. Dedic. 35, 193–228 (1990).
Cossidente A.: Hyperovals on \({\cal {H}}(3, q^2)\). J. Comb. Theory Ser. A 118, 1190–1195 (2011).
Cossidente A., Ebert G.L.: Permutable polarities and a class of ovoids of the Hermitian surface. Eur. J. Comb. 25(7), 1059–1066 (2004).
Cossidente A., King O.H., Marino G.: Hyperovals of \({\cal {H}}(3, q^2)\), when \(q\) is even. J. Comb. Theory Ser. A 120(6), 1131–1140 (2013).
Cossidente A., Marino G.: Singer action on \({\cal {H}}(3, q^2)\), \(q\) even. Preprint.
De Bruyn B.: On hyperovals of polar spaces. Des. Codes Cryptogr. 56(2–3), 183–195 (2010).
Del Fra A., Ghinelli D., Payne S.E.: \((0, n)\)-sets in a generalized quadrangle, Combinatorics ’90 (Gaeta, 1990). Ann. Discret. Math. 52, 139–157 (1992).
Makhnev A.A.: Extensions of \(GQ(4,2)\), the description of hyperovals. Discret. Math. Appl. 7(4), 419–435 (1997).
Payne S.E., Thas J.A.: Finite Generalized Quadrangles. Research Notes in Mathematics 110. Pitman, London (1984).
Segre B.: Forme e geometrie hermitiane con particolare riguardo al caso finito. Ann. Mat. Pura Appl. 70, 1–201 (1965).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by T. Penttila.
Rights and permissions
About this article
Cite this article
Cossidente, A., Pavese, F. New infinite families of hyperovals on \(\mathcal H (3,q^2), q\) odd. Des. Codes Cryptogr. 73, 217–222 (2014). https://doi.org/10.1007/s10623-013-9818-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-013-9818-3