Algebraic Geometric Codes
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Algebraic Geometric Codes
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Author : M. Tsfasman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Algebraic Geometric Codes written by M. Tsfasman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
'Et moi ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d' etre of this series.
Handbook Of Coding Theory
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Author : Vera Pless
language : en
Publisher: North Holland
Release Date : 1998-11-16
Handbook Of Coding Theory written by Vera Pless and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-16 with Computers categories.
Algebraic Function Fields And Codes
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Author : Henning Stichtenoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Algebraic Function Fields And Codes written by Henning Stichtenoth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Mathematics categories.
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.
Codes On Algebraic Curves
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Author : Serguei A. Stepanov
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-31
Codes On Algebraic Curves written by Serguei A. Stepanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-31 with Computers categories.
This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.
Advances In Algebraic Geometry Codes
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Author : Edgar Martinez-moro
language : en
Publisher: World Scientific
Release Date : 2008-10-08
Advances In Algebraic Geometry Codes written by Edgar Martinez-moro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-08 with Mathematics categories.
Advances in Algebraic Geometry Codes presents the most successful applications of algebraic geometry to the field of error-correcting codes, which are used in the industry when one sends information through a noisy channel. The noise in a channel is the corruption of a part of the information due to either interferences in the telecommunications or degradation of the information-storing support (for instance, compact disc). An error-correcting code thus adds extra information to the message to be transmitted with the aim of recovering the sent information. With contributions from renowned researchers, this pioneering book will be of value to mathematicians, computer scientists, and engineers in information theory.
Algebraic Geometry For Coding Theory And Cryptography
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Author : Everett W. Howe
language : en
Publisher: Springer
Release Date : 2017-11-15
Algebraic Geometry For Coding Theory And Cryptography written by Everett W. Howe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-15 with Mathematics categories.
Covering topics in algebraic geometry, coding theory, and cryptography, this volume presents interdisciplinary group research completed for the February 2016 conference at the Institute for Pure and Applied Mathematics (IPAM) in cooperation with the Association for Women in Mathematics (AWM). The conference gathered research communities across disciplines to share ideas and problems in their fields and formed small research groups made up of graduate students, postdoctoral researchers, junior faculty, and group leaders who designed and led the projects. Peer reviewed and revised, each of this volume's five papers achieves the conference’s goal of using algebraic geometry to address a problem in either coding theory or cryptography. Proposed variants of the McEliece cryptosystem based on different constructions of codes, constructions of locally recoverable codes from algebraic curves and surfaces, and algebraic approaches to the multicast network coding problem are only some of the topics covered in this volume. Researchers and graduate-level students interested in the interactions between algebraic geometry and both coding theory and cryptography will find this volume valuable.
Codes And Curves
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Author : Judy L. Walker
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Codes And Curves written by Judy L. Walker and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.
Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above it discussed."--BOOK JACKET.
Effective Methods In Algebraic Geometry
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Author : Teo Mora
language : en
Publisher: Springer Science & Business Media
Release Date : 1991
Effective Methods In Algebraic Geometry written by Teo Mora and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The symposium "MEGA-90 - Effective Methods in Algebraic Geome try" was held in Castiglioncello (Livorno, Italy) in April 17-211990. The themes - we quote from the "Call for papers" - were the fol lowing: - Effective methods and complexity issues in commutative algebra, pro jective geometry, real geometry, algebraic number theory - Algebraic geometric methods in algebraic computing Contributions in related fields (computational aspects of group theory, differential algebra and geometry, algebraic and differential topology, etc.) were also welcome. The origin and the motivation of such a meeting, that is supposed to be the first of a series, deserves to be explained. The subject - the theory and the practice of computation in alge braic geometry and related domains from the mathematical viewpoin- has been one of the themes of the symposia organized by SIGSAM (the Special Interest Group for Symbolic and Algebraic Manipulation of the Association for Computing Machinery), SAME (Symbolic and Algebraic Manipulation in Europe), and AAECC (the semantics of the name is vary ing; an average meaning is "Applied Algebra and Error Correcting Codes").
Using Algebraic Geometry
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Author : David A. Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Using Algebraic Geometry written by David A. Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Gr"obner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility. The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Gr"obner bases. The book does not assume the reader is familiar with more advanced concepts such as modules.
Algebraic Geometry Codes Advanced Chapters
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Author : Michael Tsfasman
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-02
Algebraic Geometry Codes Advanced Chapters written by Michael Tsfasman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-02 with Computers categories.
Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to local_libraryBook Catalogseveral domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes. The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.