Book Review
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MathSciNet review:
1567995
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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.
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.
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
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
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, 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, 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
Gilles Lachaud, Les codes géométriques de Goppa, Astérisque 133-134 (1986), 189–207 (French). Seminar Bourbaki, Vol. 1984/85. MR 837220
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, DOI 10.1007/978-94-011-3810-9
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, DOI 10.1002/mana.19821090103
[13] G. van der Geer and J. H. van Lint, Introduction to coding theory and algebraic geometry, Birkhaüser, Basel 1988.
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, DOI 10.1007/978-1-4613-8994-1_{1}2
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, DOI 10.1109/TIT.1987.1057320
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.
- [1]
- T. Beth, Some aspects of coding theory between probability, algebra, combinatorics and complexity theory, Combinatorial Theory, Lecture Notes in Math., vol. 969, Springer, Berlin and New York, 1982, pp. 12-29. MR 692231 (84j:94027)
- [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 (F. C. Holroyd and R. J. Wilson, eds.), Pitman, New York and London, 1984, pp. 35-53. MR 777155 (86m:94035)
- [6]
- -, Codes and curves, Finite Geometries, Buildings and Related Topics, Oxford Univ Press, London and New York, 1990, pp. 129-144. MR 1072160 (91j:94025)
- [7]
- Y. Ihara, Congruence relations and Shimura curves, I, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, RI, 1979, pp. 291-311. MR 546621 (81h:10039a)
- [8]
- -, Congruence relations and Shimura curves. II, J. Fac. Sci. Univ. Tokyo Sect. I A 25 (1979), 301-361. MR 523990 (81h:10039b)
- [9]
- -, Some remarks on the number of rational points of algebraic curves over finite fields, J. Fac. Sci. Univ. Tokyo Sect. I A Math 28 (1981), 721-724. MR 656048 (84c:14016)
- [10]
- G. Lachaud, Les codes géométriques de Goppa, Sém. Bourbaki 37ème année, 1984-85, No. 641, Astérisque 133-134 (1986), 189-207. MR 837220 (87f:94038)
- [11]
- M. A. Tsfasman and S. G. Vladut, Algebraic-geometric codes, Kluwer, Dordoecht, 1991. MR 1186841 (93i:94023)
- [12]
- M. A. Tsfasman, S. G. Vladut, and T. Zink, Modular curves, Shimura curves and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachr. 109 (1982), 21-28. MR 705893 (85i:11108)
- [13]
- G. van der Geer and J. H. van Lint, Introduction to coding theory and algebraic geometry, Birkhaüser, Basel 1988.
- [14]
- J. H. van Lint, Algebraic geometric codes, Coding Theory and Design Theory, Part I, IMA Math. Appl., vol. 20, Springer, New York, 1990, pp. 137-162. MR 1047878 (91d:14008)
- [15]
- J. H. van Lint and T. A. Springer, Generalized Reed-Solomon codes from algebraic geometry, IEEE Trans. Inform. Theory 33 (1987), 305-309. MR 885397 (88f:94040)
- [16]
- S. G. Vladut and Y. I. Manin, Linear codes and modular curves, J. Soviet Math. 30 (1985), 2611-2643. MR 770943 (86h:94024)
- [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