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Coding Theory and Algebraic Geometry: Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991 de Henning Stichtenoth

Coding Theory and Algebraic Geometry: Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991: Lecture Notes in Mathematics, cartea 1518

Editat de Henning Stichtenoth, Michael A. Tsfasman
en Limba Engleză Paperback – 5 aug 1992
About ten years ago, V.D. Goppa found a surprisingconnection between the theory of algebraic curves over afinite field and error-correcting codes. The aim of themeeting "Algebraic Geometry and Coding Theory" was to give asurvey on the present state of research in this field andrelated topics. The proceedings contain research papers onseveral aspects of the theory, among them: Codes constructedfrom special curves and from higher-dimensional varieties,Decoding of algebraic geometric codes, Trace codes, Exponen-tial sums, Fast multiplication in finite fields, Asymptoticnumber of points on algebraic curves, Sphere packings.
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Specificații

ISBN-13: 9783540556510
ISBN-10: 3540556516
Pagini: 240
Ilustrații: VIII, 232 p.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.34 kg
Ediția:1992
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

Algebraic geometry and coding theory an introduction.- Reed-Muller codes associated to projective algebraic varieties.- Decoding Algebraic-Geometric Codes by solving a key equation.- On the different of abelian extensions of global fields.- Goppa codes and Weierstrass gaps.- On a characterization of some minihypers in PG(t,q) (q=3 or 4) and its applications to error-correcting codes.- Deligne-Lusztig varieties and group codes.- Spectra of linear codes and error probability of decoding.- On the true minimum distance of Hermitian codes.- Sphere packings centered at S-units of algebraic tori.- A function field related to the Ree group.- On the gonality of curves, abundant codes and decoding.- Curves with many points and multiplication in finite fileds.- The domain of covering codes.- Some remarks on the asymptotic number of points.- On the weights of trace codes.- Minoration de Certaines Sommes Exponentielles Binaires.- Linear codes, strata of Grassmannians, and the problems of segre.