Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: C. J. Moreno
Title: Algebraic curves over finite fields
Additional book information: Cambridge University Press, Cambridge, 1991, ix+246 pp.\ US$49.50. ISBN 0-521-34252-X.

References [Enhancements On Off] (What's this?)

  • [1] Thomas Beth, Some aspects of coding theory between probability, algebra, combinatorics and complexity theory, Combinatorial theory (Schloss Rauischholzhausen, 1982) Lecture Notes in Math., vol. 969, Springer, Berlin-New York, 1982, pp. 12–29. MR 692231
  • [2] Y. Driencourt and J. F. Michon, Rapport sur les codes géométriques, Université d'Aix-Marseille II and Université de Paris VII.
  • [3] V. D. Goppa, Algebraico-geometric codes, Math. USSR-Ivz 21 (1983), 75-91.
  • [4] -, Codes and information, Russian Math. Surveys 39 (1984), 87-141.
  • [5] J. W. P. Hirschfeld, Linear codes and algebraic curves, Geometrical combinatorics (Milton Keynes, 1984) Res. Notes in Math., vol. 114, Pitman, Boston, MA, 1984, pp. 35–53. MR 777155
  • [6] J. W. P. Hirschfeld, Codes and curves, Finite geometries, buildings, and related topics (Pingree Park, CO, 1988) Oxford Sci. Publ., Oxford Univ. Press, New York, 1990, pp. 129–144. MR 1072160
  • [7] Yasutaka Ihara, Congruence relations and Shimūra curves, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 291–311. MR 546621
    Yasutaka Ihara, Congruence relations and Shimūra curves. II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 25 (1979), no. 3, 301–361. MR 523990
  • [8] Yasutaka Ihara, Congruence relations and Shimūra curves, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 291–311. MR 546621
    Yasutaka Ihara, Congruence relations and Shimūra curves. II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 25 (1979), no. 3, 301–361. MR 523990
  • [9] 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
  • [10] Gilles Lachaud, Les codes géométriques de Goppa, Astérisque 133-134 (1986), 189–207 (French). Seminar Bourbaki, Vol. 1984/85. MR 837220
  • [11] M. A. Tsfasman and S. G. Vlăduţ, Algebraic-geometric codes, Mathematics and its Applications (Soviet Series), vol. 58, Kluwer Academic Publishers Group, Dordrecht, 1991. Translated from the Russian by the authors. MR 1186841
  • [12] M. A. Tsfasman, S. G. Vlăduţ, and Th. Zink, Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachr. 109 (1982), 21–28. MR 705893, https://doi.org/10.1002/mana.19821090103
  • [13] G. van der Geer and J. H. van Lint, Introduction to coding theory and algebraic geometry, Birkhaüser, Basel 1988.
  • [14] Jacobus H. van Lint, Algebraic geometric codes, Coding theory and design theory, Part I, IMA Vol. Math. Appl., vol. 20, Springer, New York, 1990, pp. 137–162. MR 1047878, https://doi.org/10.1007/978-1-4613-8994-1_12
  • [15] J. H. van Lint and T. A. Springer, Generalized Reed-Solomon codes from algebraic geometry, IEEE Trans. Inform. Theory 33 (1987), no. 3, 305–309. MR 885397, https://doi.org/10.1109/TIT.1987.1057320
  • [16] S. G. Vlèduts and Yu. I. Manin, Linear codes and modular curves, Current problems in mathematics, Vol. 25, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, pp. 209–257 (Russian). MR 770943
  • [17] J. F. Voloch, Codes and curves, Eureka 43 (1983), 53-61.
  • [18] M. Wirtz, Verallegemeinerte Goppa-Codes, Diplomarbeit, Universität Munster, 1986.

Review Information:

Reviewer: J. W. P. Hirschfeld
Journal: Bull. Amer. Math. Soc. 27 (1992), 327-332
DOI: https://doi.org/10.1090/S0273-0979-1992-00321-X