Coding Theory and Algebraic Geometry
Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991
(Sprache: Englisch)
About ten years ago, V.D. Goppa found a surprising
connection between the theory of algebraic curves over a
finite field and error-correcting codes. The aim of the
meeting "Algebraic Geometry and Coding Theory" was to give a
survey on the present...
connection between the theory of algebraic curves over a
finite field and error-correcting codes. The aim of the
meeting "Algebraic Geometry and Coding Theory" was to give a
survey on the present...
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Klappentext zu „Coding Theory and Algebraic Geometry “
About ten years ago, V.D. Goppa found a surprisingconnection between the theory of algebraic curves over a
finite field and error-correcting codes. The aim of the
meeting "Algebraic Geometry and Coding Theory" was to give a
survey on the present state of research in this field and
related topics. The proceedings contain research papers on
several aspects of the theory, among them: Codes constructed
from special curves and from higher-dimensional varieties,
Decoding of algebraic geometric codes, Trace codes, Exponen-
tial sums, Fast multiplication in finite fields, Asymptotic
number of points on algebraic curves, Sphere packings.
Inhaltsverzeichnis zu „Coding Theory and Algebraic Geometry “
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.
Bibliographische Angaben
- 1992, 240 Seiten, Masse: 15,5 x 23,5 cm, Taschenbuch, Englisch
- Herausgegeben: Michael A. Tsfasman, Henning Stichtenoth
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3540556516
- ISBN-13: 9783540556510
- Erscheinungsdatum: 05.08.1992
Sprache:
Englisch
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