Coding Theory and Algebraic Geometry
Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991
Published on 5. August 1992
Book
Paperback/Softback
VIII, 232 pages
978-3-540-55651-0 (ISBN)
Description
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.
More details
Series
Edition
1992 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 232 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 14 mm
Weight
371 gr
ISBN-13
978-3-540-55651-0 (9783540556510)
DOI
10.1007/BFb0087986
Schweitzer Classification
Content
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.