Coding Theory and Algebraic Geometry

Proceedings of the International Workshop held in Luminy, France, June 17-21, 1991

Author: Henning Stichtenoth,Michael A. Tsfasman

Publisher: Springer

ISBN: 3540472673

Category: Mathematics

Page: 232

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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.
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Algebra for Secure and Reliable Communication Modeling

Author: Mustapha Lahyane, Edgar Martínez-Moro

Publisher: American Mathematical Soc.

ISBN: 1470410184

Category: Geometry, Algebraic

Page: 240

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This volume contains the proceedings of the CIMPA Research School and Conference on Algebra for Secure and Reliable Communication Modeling, held from October 1-13, 2012, in Morelia, State of Michoacán, Mexico. The papers cover several aspects of the theory of coding theory and are gathered into three categories: general theory of linear codes, algebraic geometry and coding theory, and constacyclic codes over rings. The aim of this volume is to fill the gap between the theoretical part of algebraic geometry and the applications to problem solving and computational modeling in engineering, signal processing and information theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).
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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

18th International Symposium, AAECC-18, Tarragona, Sapin, June 8-12, 2009, Proceedings

Author: Maria Bras-Amorós,Tom Høholdt

Publisher: Springer Science & Business Media

ISBN: 3642021808

Category: Computers

Page: 243

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The AAECC symposia serieswas started in 1983by Alain Poli (Toulouse), who, together with R. Desq, D. Lazardand P. Camion, organizedthe ?rst conference. OriginallytheacronymAAECCstoodfor"AppliedAlgebraandError-Correcting Codes."Overtheyearsitsmeaninghasshiftedto"AppliedAlgebra, Algebraic- gorithmsandError-CorrectingCodes,"re?ectingthegrowingimportanceofc- plexity, particularlyfor decoding algorithms.During the AAECC-12 symposium the ConferenceCommitteedecidedtoenforcethe theoryandpracticeofthe c- ing side as well as the cryptographic aspects. Algebra was conserved, as in the past, but slightly more oriented to algebraic geometry codes, ?nite ?elds, c- plexity, polynomials, andgraphs. The main topics for AAECC-18 were algebra, algebraiccomputation, codes and algebra, codes and combinatorics, modulation and codes, sequences, and cryptography. TheinvitedspeakersofthiseditionwereIwanDuursma, HenningStichtenoth, and Fernando Torres. We would like to express our deep regret for the loss of Professor Ralf Kotter, ] who recently passed away and could not be our fourth invited speaker. Except for AAECC-1 (Discrete Mathematics 56, 1985) and AAECC-7 (D- crete Applied Mathematics 33, 1991), the proceedings of all the symposia have been published in Springer'sLecture Notes in Computer Science (Vols. 228,229, 307, 356, 357, 508, 539, 673, 948, 1255, 1719, 2227, 2643, 3857, 4851). Itis apolicy ofAAECCto maintaina highscienti?c standard, comparableto that of a journal. This was made possible thanks to the many referees involved. Each submitted paper was evaluated by at least two international researchers. AAECC-18 received and refereed 50 submissions. Of these, 22 were selected for publication in these proceedings as regular papers and 7 were selected as extended abstracts.
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Algebraic Geometry in Coding Theory and Cryptography

Author: Harald Niederreiter,Chaoping Xing

Publisher: Princeton University Press

ISBN: 9781400831302

Category: Mathematics

Page: 272

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This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
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Applications of Algebraic Geometry to Coding Theory, Physics and Computation

Author: Ciro Ciliberto,Friedrich Hirzebruch,Rick Miranda,Mina Teicher

Publisher: Springer Science & Business Media

ISBN: 9401010110

Category: Mathematics

Page: 337

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An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.
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Coding theory, design theory, group theory

proceedings of the Marshall Hall Conference

Author: Marshall Hall,Dieter Jungnickel,Scott A. Vanstone

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 299

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Contains papers prepared for the 1990 multidisciplinary conference held to honor the late mathematician and researcher. Topics include applications of classic geometry to finite geometries and designs; multiple transitive permutation groups; low dimensional groups and their geometry; difference sets in 2-groups; construction of Galois groups; construction of strongly p-imbeded subgroups in finite simple groups; Hall triple systems, Fisher spaces and 3-transposition groups; explicit embeddings in finitely generated groups; 2-transitive and flag transitive designs; efficient representations of perm groups; codes and combinatorial designs; optimal normal bases for finite fields; vector space designs from quadratic forms and inequalities; primitive permutation groups, graphs and relation algebras; large sets of ordered designs, orthogonal 1-factorizations and hyperovals; algebraic integers all of whose algebraic conjugates have the same absolute value.
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Algebraic K-Theory and Its Applications

Author: Jonathan Rosenberg

Publisher: Springer Science & Business Media

ISBN: 9780387942483

Category: Mathematics

Page: 394

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Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
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Algebraic Function Fields and Codes

Author: Henning Stichtenoth

Publisher: Springer Science & Business Media

ISBN: 3540768777

Category: Mathematics

Page: 360

View: 1930

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This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
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