Coding Theory and Algebraic Geometry Proceedings of the International Workshop held in Luminy, France, June 17–21, 1991 / [electronic resource] :
edited by Henning Stichtenoth, Michael A. Tsfasman.
- Berlin, Heidelberg : Springer Berlin Heidelberg, 1992.
- VIII, 232 p. online resource.
- Lecture Notes in Mathematics, 1518 0075-8434 ; .
- Lecture Notes in Mathematics, 1518 .
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.
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.
9783540472674
10.1007/BFb0087986 doi
Mathematics.
Chemistry--Mathematics.
Geometry, algebraic.
Number theory.
Mathematics.
Algebraic Geometry.
Number Theory.
Math. Applications in Chemistry.
Numerical and Computational Methods in Engineering.
QA564-609
516.35
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.
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.
9783540472674
10.1007/BFb0087986 doi
Mathematics.
Chemistry--Mathematics.
Geometry, algebraic.
Number theory.
Mathematics.
Algebraic Geometry.
Number Theory.
Math. Applications in Chemistry.
Numerical and Computational Methods in Engineering.
QA564-609
516.35