Abstract
In this chapter some of the basic concepts of algebraic geometry needed for algebraic geometric codes will be presented. Since the theory of algebraic geometry is both vast and deep, we can only give a rough outline here. Emphasis will be placed on making the ideas intuitive and clear enough to enable the reader to understAnd the algebraic geometric codes. The majority of this chapter is based on the treatment of Fulton [2]. For a more complete treatment of algebraic geometry the reader should consult that reference, or the recent book by Moreno [4]. Some other stAndard textbooks in algebraic geometry are [1, 3, 7, 9].
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Chevalley, Introduction to the Theory of Algebraic Functions of One Variable, A.M.S. Math. Surveys, New York, 1951.
W. Fulton, Algebraic Curves, Benjamin, New York, 1969.
R. Hartshorne, Algebraic Geometry, Springer-Verlag, New York, 1977.
C. Moreno, Algebraic Curves over Finite Fields, Cambridge University Press, 1991.
J.-P. Serre, “Sur le nombre de points rationnels d’une corbe algébrique sur un corps fini”, C.R. Acad. Sci. Paris Sér. 1, 296 (1983), 397–402.
J.-P. Serre, “Nombres de points des courbes algébriques sur F q ” Séminaire de Théorie des Nombres, Bordeaux, 22 (1983), 1–8.
I. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, New York, 1977.
J.H. Van Lint and G. Van Der Geer, Introduction to Coding Theory and Algebraic Geometry, Dmv Seminar, BAnd 12, Birkhauser Verlag, 1988.
R.J. Walker, Algebraic Curves, Dover, New York, 1962.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media New York
About this chapter
Cite this chapter
Blake, I.F., Gao, X., Mullin, R.C., Vanstone, S.A., Yaghoobian, T. (1993). Introduction to Algebraic Geometry. In: Menezes, A.J. (eds) Applications of Finite Fields. The Springer International Series in Engineering and Computer Science, vol 199. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2226-0_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2226-0_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5130-4
Online ISBN: 978-1-4757-2226-0
eBook Packages: Springer Book Archive