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Coding theory and algebraic geometry : proceedings of the international workshop held in Luminy, France, June 17-21, 1991 / H. Stichtenoth, M.A. Tsfasman (eds.).

Contributor(s): Stichtenoth, H. (Henning), 1944- | Tsfasman, M. A. (Michael A.), 1954-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1518.Publisher: Berlin ; New York : Springer-Verlag, ©1992Description: 1 online resource (viii, 223 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540472674; 3540472673Subject(s): Coding theory -- Congresses | Geometry, Algebraic -- Congresses | Géométrie algébrique -- Congrès | Codage -- Histoire | Coding theory | Geometry, Algebraic | Codierungstheorie | Algebraische Geometrie | KongressGenre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Print version:: Coding theory and algebraic geometry.DDC classification: 629.8/312 LOC classification: QA3 | .L28 no. 1518 | QA268Online resources: Click here to access online
Contents:
Algebraic geometry and coding theory / H. Stichtenoth, M.A. Tsfasman -- Reed-Muller codes associated to projective algebraic varieties / Y. Aubry -- Decoding algebraic-geometric codes by solving a key equation / D. Ehrhard -- On the different of abelian extensions of global fields / G. Frey, M. Perret, H. Stichtenoth -- Goppa codes and Weierstrass gaps / A. Garcia, R. Lax -- On a characterization of some minihypers in PG(t, q) (q = 3 or 4) and its applications to error-correcting codes / N. Hamada, T. Helleseth -- Deligne-Lusztig varieties and group codes / J.P. Hansen -- Spectra of linear codes and error probability of decoding / G.L. Katsman, M.A. Tsfasman, S.G. Vladut -- On the true minimum distance of hermitian codes / P.V. Kumar, K. Yang -- Sphere packings centered at S-units of algebraic tori / B.E. Kunyavskii -- A function field related to the Ree group / J.P. Pedersen -- On the gonality of curves, abundant codes and decoding / R. Pellikaan -- Curves with many points and multiplication in finite fields / I.E. Shparlinksi, M.A. Tsfasman, S.G. Vladut -- The domain of covering codes / P. Stokes -- Some remarks on the asymptotic number of points / M.A. Tsfasman -- On the weights of trace codes / C. Voss -- Minoration de certaines sommes exponentielles binaires / F. Rodier -- Linear codes, strata of grassmannians, and the problem of segre / A.N. Skorobogatov.
Action note: digitized 2010 committed to preserveSummary: 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.
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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.

Algebraic geometry and coding theory / H. Stichtenoth, M.A. Tsfasman -- Reed-Muller codes associated to projective algebraic varieties / Y. Aubry -- Decoding algebraic-geometric codes by solving a key equation / D. Ehrhard -- On the different of abelian extensions of global fields / G. Frey, M. Perret, H. Stichtenoth -- Goppa codes and Weierstrass gaps / A. Garcia, R. Lax -- On a characterization of some minihypers in PG(t, q) (q = 3 or 4) and its applications to error-correcting codes / N. Hamada, T. Helleseth -- Deligne-Lusztig varieties and group codes / J.P. Hansen -- Spectra of linear codes and error probability of decoding / G.L. Katsman, M.A. Tsfasman, S.G. Vladut -- On the true minimum distance of hermitian codes / P.V. Kumar, K. Yang -- Sphere packings centered at S-units of algebraic tori / B.E. Kunyavskii -- A function field related to the Ree group / J.P. Pedersen -- On the gonality of curves, abundant codes and decoding / R. Pellikaan -- Curves with many points and multiplication in finite fields / I.E. Shparlinksi, M.A. Tsfasman, S.G. Vladut -- The domain of covering codes / P. Stokes -- Some remarks on the asymptotic number of points / M.A. Tsfasman -- On the weights of trace codes / C. Voss -- Minoration de certaines sommes exponentielles binaires / F. Rodier -- Linear codes, strata of grassmannians, and the problem of segre / A.N. Skorobogatov.

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