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Book Review

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Book Information

Author(s): Oliver Pretzel
Title: Codes and algebraic curves
Additional book information: Oxford Lecture Series in Mathematics and Its Applications, Clarendon Press, Oxford, 1998, xii + 192, $65.00, ISBN 0-19-850039-4

References:

[1]
S. S. Abhyankar, Historical ramblings in algebraic geometry and related algebra, Amer. Math. Soc. Monthly, vol. 83 (1976), 409-448. MR 53:5581

[2]
E. Bombieri, Counting points on curves over finite fields (d'aprés S. A. Stepanov), Sem. Bourbaki, No. 430 (1972/73). MR 55:2912

[3]
C. Chevalley, Introduction to the Theory of Functions of One Variable, Amer. Math. Soc. Math Surveys, New York, 1951. MR 13:64a

[4]
V. D. Goppa, Geometry and Codes, Mathematics and its Applications, vol. 24, Kluwer, Dordrecht, 1991. MR 91a:14013

[5]
V. D. Goppa, Decoding and diophantine approximations, Problems of Control and Information Theory, vol. 5 (1976), 195-206. MR 56:11511

[6]
T. Hoholdt, J. van Lint, and R. Pellikan, Algebraic geometry codes, Handbook of Coding Theory (V. S. Pless, W. C. Huffman, Eds.), Elsevier, 1998. CMP 99:07

[7]
Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo, vol. 28 (1981), 721-724. MR 84c:14016

[8]
Y. I. Manin, What is the maximum number of points on a curve over $F$? J. Fac. Sci. Univ. Tokyo, vol. 28 (1981), 715-720. MR 84c:14015

[9]
B. Mazur, Arithmetic on curves, A.M.S. Colloquium Lectures, Bull. Amer. Math. Soc., vol. 14, no. 2 (1986), 206-259. MR 88e:11050

[10]
J.-P. Serre, Sur le nombre des points rationnels d'une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I, vol. 296 (1983), 397-402. MR 85b:14027

[11]
C. Shannon, A mathematical theory of communication, Bell. System Tech. J., vol. 27 (1948), 379-423, 623-656. MR 10:133e

[12]
T. M. Thompson, From Error Correcting Codes through Sphere Packings to Simple Groups, The Carus Mathematical Monographs, vol. 21, Mathematical Association of America, Washington, DC, 1983. MR 86j:94002

[13]
A. Weil, Sur les Courbes Algebriques et les Variétés qui s'en Deduisent, Hermann, Paris, 1948.

[14]
A. Weil, Review of ``Introduction to the theory of algebraic functions, by C. Chevalley'', Bull. Amer. Math. Soc., vol. 57 (1951), 384-398.

Additional Information:

Reviewer(s):
Carlos Moreno
Affiliation: City University of New York
Email: carlos@kepler.baruch.cuny.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 36 (1999), 399-404.

MSC (1991): Primary 94B27, 11T71, 14H05
DOI: 10.1090/S0273-0979-99-00783-1
PII: S 0273-0979(99)00783-1
Posted: June 8, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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