Codes On Algebraic Curves
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Codes And Algebraic Curves
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Author : Oliver Pretzel
language : en
Publisher: Clarendon Press
Release Date : 1998-01-08
Codes And Algebraic Curves written by Oliver Pretzel and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-08 with Mathematics categories.
The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.
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.
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.
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 Codes On Lines Planes And Curves
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Author : Richard E. Blahut
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-03
Algebraic Codes On Lines Planes And Curves written by Richard E. Blahut and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-03 with Technology & Engineering categories.
The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.
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 : 2012-12-06
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 2012-12-06 with Mathematics 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.
Rational Algebraic Curves
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Author : J. Rafael Sendra
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-10
Rational Algebraic Curves written by J. Rafael Sendra 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 2007-12-10 with Mathematics categories.
The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.