Coding theory and algebraic geometry : proceedings of the international workshop held in Luminy, France, June 17-21, 1991
著者
書誌事項
Coding theory and algebraic geometry : proceedings of the international workshop held in Luminy, France, June 17-21, 1991
（Lecture notes in mathematics, 1518）
Springer-Verlag, c1992
- : gw
- : us
大学図書館所蔵 全84件
注記
Includes bibliographical references
"The workshop 'Algebraic Geometry and Coding Theory-3' organized by the Institute of Information Transmission(Moscow),University of Essen,Équipe Arithmétique et Théorie de l'Information de C.N.R.S(Marseille-Luminy),and Group d'Etude du Codage de Toulon took placein the Centre International de Rencontres Mathématiques" -- Foreword
"The workshop was a continuation of AGCT-1 and AGCT-2 that took place in 1987 and 1989" -- Foreword
内容説明・目次
内容説明
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 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.
目次
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.
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