Full 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.
Contents
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.
