Curves in a hyperbolic quadric surface with a large number of \({\mathbb{F}_{q}}\)-points
Article
First Online:
Received:
Revised:
- 50 Downloads
Abstract
Here we study curves C over \({\mathbb{F}_q}\) contained in a hyperbolic quadric surface and such that \({\sharp (C(\mathbb{F}_q))}\) is large.
Mathematics Subject Classification (2010)
14G15 14H99Keywords
Hyperbolic quadric surface Curve over a finite fieldReferences
- 1.Couvreur, A., Duursma, I.: Evaluation codes from smooth quadric surfaces and twisted Segre varieties. arXiv:1101.4603v1.Google Scholar
- 2.Edoukou F.A.B.: Codes defined by forms of degree 2 on quadric surfaces. IEEE Trans. Inform. Theory 54, 860–864 (2008)MathSciNetCrossRefGoogle Scholar
- 3.Edoukou F.A.B., Hallez A., Rodier F., Storme L.: A study of intersections of quadrics having applications on the small weight codewords of the functional codes C 2(Q), Q a non-singular quadric. J. Pure Appl. Algebra 214, 1729–1739 (2010)MathSciNetMATHCrossRefGoogle Scholar
- 4.Edoukou F.A.B., Hallez A., Rodier F., Storme L.: The small weight codewords of the functional codes associated to non-singular Hermitian varieties. Des. Codes Cryptogr. 56, 219–233 (2010)MathSciNetMATHCrossRefGoogle Scholar
- 5.Hartshorne R.: Algebraic Geometry. Springer, Berlin (1977)MATHGoogle Scholar
- 6.Hirschfeld J.W.P.: Finite Projective Spaces of Three Dimensions. Clarendon Press, Oxford (1985)MATHGoogle Scholar
- 7.Homma M., Kim S.J.: Around Sziklai’s conjecture on the number of points of a plane curve over a finite field. Finite Fields Appl. 15, 468–474 (2009)MathSciNetMATHCrossRefGoogle Scholar
- 8.Homma M., Kim S.J.: Sziklai’s conjecture on the number of points of a plane curve over a finite field III. Finite Fields Appl. 16, 315–319 (2010)MathSciNetMATHCrossRefGoogle Scholar
- 9.Sampson J.H., Washnitzer G.: A Künneth formula for coherent algebraic sheaves. Ill. J. Math. 3, 389–402 (1959)MathSciNetMATHGoogle Scholar
- 10.Stichtenoth H.: Algebraic Function Fields and Codes. 2nd edn. Springer, Berlin (2009)MATHGoogle Scholar
Copyright information
© Springer Basel AG 2011