Book Review
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Book Information:
Author:
Oliver Pretzel
Title:
Codes and algebraic curves
Additional book information:
Oxford Lecture Series in Mathematics and Its Applications, Clarendon Press,
Oxford,
1998,
xii + 192 pp.,
ISBN 0-19-850039-4,
$65.00$
Shreeram S. Abhyankar, Historical ramblings in algebraic geometry and related algebra, Amer. Math. Monthly 83 (1976), no. 6, 409–448. MR 401754, DOI 10.2307/2318338
Enrico Bombieri, Counting points on curves over finite fields (d’après S. A. Stepanov), Séminaire Bourbaki, 25ème année (1972/1973), Exp. No. 430, Lecture Notes in Math., Vol. 383, Springer, Berlin, 1974, pp. 234–241. MR 0429903
C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
V. D. Goppa, Geometry and codes, Mathematics and its Applications (Soviet Series), vol. 24, Kluwer Academic Publishers Group, Dordrecht, 1988. Translated from the Russian by N. G. Shartse. MR 1029027, DOI 10.1007/978-94-015-6870-8
V. D. Goppa, Decoding and Diophantine approximations, Problems of Control and Information Theory/Problemy Upravlenija i Teorii Informacii 5 (1976), no. 3, 195–206 (Russian, with English summary). MR 0453244
[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
Yasutaka Ihara, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 721–724 (1982). MR 656048
Yu. I. Manin, What is the maximum number of points on a curve over $\textbf {F}_{2}$?, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 715–720 (1982). MR 656047
Barry Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 207–259. MR 828821, DOI 10.1090/S0273-0979-1986-15430-3
Jean-Pierre Serre, Sur le nombre des points rationnels d’une courbe algébrique sur un corps fini, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 9, 397–402 (French, with English summary). MR 703906
Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
Thomas M. Thompson, From error-correcting codes through sphere packings to simple groups, Carus Mathematical Monographs, vol. 21, Mathematical Association of America, Washington, DC, 1983. MR 749038
[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.
- [1]
- S. S. Abhyankar, Historical ramblings in algebraic geometry and related algebra, Amer. Math. Soc. Monthly, vol. 83 (1976), 409-448. MR 0401754
- [2]
- E. Bombieri, Counting points on curves over finite fields (d'aprés S. A. Stepanov), Sem. Bourbaki, No. 430 (1972/73). MR 0429903
- [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 1029027
- [5]
- V. D. Goppa, Decoding and diophantine approximations, Problems of Control and Information Theory, vol. 5 (1976), 195-206. MR 0453244
- [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 0656048
- [8]
- Y. I. Manin, What is the maximum number of points on a curve over
? J. Fac. Sci. Univ. Tokyo, vol. 28 (1981), 715-720. MR 0656047
- [9]
- B. Mazur, Arithmetic on curves, A.M.S. Colloquium Lectures, Bull. Amer. Math. Soc., vol. 14, no. 2 (1986), 206-259. MR 0828821
- [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 0703906
- [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 0749038
- [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.
Review Information:
Reviewer:
Carlos Moreno
Affiliation:
City University of New York
Email:
carlos@kepler.baruch.cuny.edu
Journal:
Bull. Amer. Math. Soc.
36 (1999), 399-404
DOI:
https://doi.org/10.1090/S0273-0979-99-00783-1
Published electronically:
June 8, 1999
Review copyright:
© Copyright 1999
American Mathematical Society
