Les codes géométriques de Goppa

Gilles Lachaud

Séminaire Bourbaki (1984-1985)

  • Volume: 27, page 189-207
  • ISSN: 0303-1179

How to cite

top

Lachaud, Gilles. "Les codes géométriques de Goppa." Séminaire Bourbaki 27 (1984-1985): 189-207. <http://eudml.org/doc/110041>.

@article{Lachaud1984-1985,
author = {Lachaud, Gilles},
journal = {Séminaire Bourbaki},
keywords = {Varshamov-Gilbert bound; algebraic curves; codes in algebraic geometries; Goppa codes},
language = {fre},
pages = {189-207},
publisher = {Société Mathématique de France},
title = {Les codes géométriques de Goppa},
url = {http://eudml.org/doc/110041},
volume = {27},
year = {1984-1985},
}

TY - JOUR
AU - Lachaud, Gilles
TI - Les codes géométriques de Goppa
JO - Séminaire Bourbaki
PY - 1984-1985
PB - Société Mathématique de France
VL - 27
SP - 189
EP - 207
LA - fre
KW - Varshamov-Gilbert bound; algebraic curves; codes in algebraic geometries; Goppa codes
UR - http://eudml.org/doc/110041
ER -

References

top
  1. [Ch] Chevalley, C., Introduction to the theory of algebraic functions of one variable, Math. Surveys, VI, Providence, A.M.S., 1951 Zbl0045.32301MR42164
  2. [Ha] Hartshorne, R., Algebraic Geometry, Graduate texts in Math., n°52, Springer, New York, 1977 Zbl0367.14001MR463157
  3. [Lan] Lang, S., Introduction to Algebraic and Abelian functions, 2d ed., Graduate texts in Math., n°89, Springer, New York, 1982 Zbl0513.14024MR681120
  4. [Se 1] Serre, J.P., Groupes algébriques et corps de classes, A.S.I.1254, Pub. Math. Univ. Nancago VII, Hermann, Paris, 1959 Zbl0097.35604MR103191
  5. [Sh] Shafarevich, I.R., Basic Algebraic Geometry, Springer, Berlin, 1977 Zbl0362.14001MR447223
  6. [We] Weil, A., Basic Number Theory, 3rd edition, Grund. der Math. Wiss., Bd.144, Springer, New York, 1974. Zbl0326.12001MR427267
  7. [B1] Blake, I.F., Algebraic coding Theory : History and Development, Dowden, Hutchinson & Ross, Stroudsburg, 1973 Zbl0279.94005MR373758
  8. [ME] McEliece, R.J., The theory of information and coding, Encyclopedia of Math., vol.,3, Reading, Addison-Wesley, 1977 Zbl0376.94011MR469516
  9. [MW-S] Macwilliams, F.J., Sloane, N.J.A., The theory of Error-Correcting codes, North-Holland, Amsterdam, 1977 Zbl0657.94010
  10. [VL] Lint, J.H. van, Introduction to Coding Theory, Graduate texts in Math.86, Springer, Berlin, 1982. Zbl0485.94015MR658134
  11. [Bo] Bombieri, E., Counting points on curves over finite fields (d'après S.A. Stepanov), Séminaire BOURBAKI, 25e année, 1972/73, n°430, Lect.Notes in Math. n°383, Springer, 1974 Zbl0307.14011MR429903
  12. [Ih] Ihara, Y., Some remarks on the number of rational points of algebraic curves over finite fields, J.Fac.Sci. Univ. Tokyo, I A, 28 (1981), 721-724 Zbl0509.14019MR656048
  13. [Laz] Lazard, D., Primitives des fonctions élémentaires (d'après Risch et Davenport), Séminaire BOURBAKI, 36e annnée, 1983/84, n°627, Astérisque, S.M.F., Paris, 1984 Zbl0583.68016
  14. [Se 2] Serre, J.P., Sur le nombre des point rationnels d'une courbe algébrique sur un corps fini, C.R.Acad.Sc. Paris, 296, (1983), 397-402 Zbl0538.14015MR703906
  15. [Se 3] Serre, J.P., Nombre de points des courbes algébriques sur Fq, Sém.Th. Nombres, Bordeaux, (1982-1983), exp.n°22 Zbl0538.14016MR750323
  16. [Se 4] Serre, J.P., Résumé du cours de l'année1984/1984, Annuaire du Collège de France, Paris, 1985 
  17. [Ta] Tate, J., Residues of differentials on curves, Ann.Sc. Ec.Norm.Sup. (4), 1 (1966), 149-159. Zbl0159.22702MR227171
  18. [Br] Broué, M., Codes Correcteurs d'Erreurs Auto-orthogonaux sur le Corps à Deux Eléments et Formes Quadratiques Entières Définies Positives à discriminant + 1, Discrete Math.17 (1977), 247-269 Zbl0358.94014MR449863
  19. [Ch-Hs] Chen, C.L., Hsiao, M.V., Error-Correcting Codes for Semiconductor Memory, I.B.M. J.Res. Develop.28 (1984), 124-134 
  20. [De-Pi] Delsarte, P., Piret, P., Algebraic constructions of Shannon codes for regular channels, I.E.E.E. Trans. Inf. Theory28 (1982), 593-599 Zbl0491.94012MR674208
  21. [Dr-Mi] Driencourt, Y., Michon, J.F., Binary Elliptic codes, prépublication, A.T.P. 399 du C.N.R.S. 
  22. [Go 1] Goppa, V.D., A Rational Representation of Codes and (L,g)-Codes, Problemy Peredachi Informatsii3 (1971), 41-49;=Probl. Inform. Transmission3 (1971), 223-229 Zbl0306.94010MR294041
  23. [Go 2] Goppa, V.D., Decoding and Diophantine approximation, Problemy Uprav. i Teor. Informatsii5 (1976), 195-206; = Problems of Control and Information Theory5 (1976), 1-12 Zbl0348.94014MR453244
  24. [Go 3] Goppa, V.D., Codes on algebraic curves, Dokl. Akad. Nauk, S.S.S.R., 259 (1981), 1289-1290, = Soviet Math. Dokl.24 (1981), 170-172 Zbl0489.94014MR628795
  25. [Go 4] Goppa, V.D., Algebraico-Geometric Codes, Izv. Akad. Nauk, S.S.S.R., 46 (1982); = Math. U.S.S.R. Izvestiya21 (1983), 75-91 Zbl0522.94013MR670165
  26. [K-T-V] Katsman, G.L., Tsfasman, M.A., Vladut, S.G., Modular Curves and Codes with a polynomial construction, I.E.E.E. Trans. Inf. Theory, 30 (1984), 353-355 Zbl0544.94016MR754865
  27. [Ma] Manin, Yu.I., What is the maximum number of points on a curve over F2 ? , J.Fac.Sci. Univ. Tokyo,I A, 28, (1981), 715-720 Zbl0527.14021MR656047
  28. [Ma-V1] Manin, Yu.I., Vladut, S.G., Codes linéaires et courbes modulaires (en russe), Sovr. Prob. Mat., VINITI, Moscou, 1984 
  29. [Mi] Michon, J.F., Les codes Géométriques de V.D.Goppa, Sém. Th. Nombres Bordeaux (1983-1984) MR784059
  30. [SKHN] Sugiyama, Y., Kasahara, M., Hirasawa, S., Namekawa, T., Further results on Goppa codes and their applications to constructing efficient binary codes, I.E.E.E. trans. Inf. Theory22 (1976), 518-525 Zbl0356.94056MR479662
  31. [Ts] Tsfasman, M.A., Goppa codes that are better than Varshamov-Gilbert bound, Prob. Peredachi Inform.18 (1982), 3-6 ; = Probl. Inform. Transmission, 18 (1982), 163-166 Zbl0531.94015MR711895
  32. [Ts-Vl-Zi] Tsfasman, M.A., Vladut, S.G., Zink, Th., Modular Curves, Shimura Curves, and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachr.109 (1982), 21-28 Zbl0574.94013MR705893
  33. [Vl-Dr] Vladut, S.G., Drinfeld, V.G., Number of Points of an Algebraic Curve, Funktsional'-nyi Analiz i Ego Prilozhenia17 (1983), 68-69; = Functional Analysis, 17 (1983), 53-54. Zbl0522.14011MR695100

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.