Paperback. About ten years ago, V.D. Goppa found a surprisingconnection between the theory of algebraic curves over afinite field and error-correcting codes. The aim of themeeting "Algebraic Geometry and Coding Theory" was to give asurvey on the present state of research in this field andrelated topics. The proceedings contain research papers onseveral aspects of the theory, among them: Codes constructedfrom special curves and from higher-dimensional varieties,Decoding of algebraic geometric codes, Trace codes, Exponen-tial sums, Fast multiplication in finite fields, Asymptoticnumber of points on algebraic curves, Sphere packings. A volume of workshop proceedings which explores several aspects of coding theory, including exponential sums, codes constructed from special curves, the decoding of algebraic geometric codes, trace codes, the asymptotic number of points on algebraic curves and sphere packings. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

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Dati bibliografici

Titolo: Coding Theory and Algebraic Geometry (Paperback)
Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
Data di pubblicazione: 1992
Lingua: Inglese
ISBN 10: 3540556516
ISBN 13: 9783540556510
Rilegatura: Paperback
Condizione: new

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Riassunto

About ten years ago, V.D. Goppa found a surprisingconnection between the theory of algebraic curves over afinite field and error-correcting codes. The aim of themeeting "Algebraic Geometry and Coding Theory" was to give asurvey on the present state of research in this field andrelated topics. The proceedings contain research papers onseveral aspects of the theory, among them: Codes constructedfrom special curves and from higher-dimensional varieties,Decoding of algebraic geometric codes, Trace codes, Exponen-tial sums, Fast multiplication in finite fields, Asymptoticnumber of points on algebraic curves, Sphere packings.

Contenuti

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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