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Author | : Serguei A. Stepanov |
Publisher | : Springer Science & Business Media |
Total Pages | : 372 |
Release | : 1999-07-31 |
Genre | : Computers |
ISBN | : 9780306461446 |
Download Codes on Algebraic Curves Book in PDF, ePub and Kindle
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.
Author | : Oliver Pretzel |
Publisher | : Clarendon Press |
Total Pages | : 209 |
Release | : 1998-01-08 |
Genre | : Mathematics |
ISBN | : 0191589047 |
Download Codes and Algebraic Curves Book in PDF, ePub and Kindle
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.
Author | : Edgar Mart¡nez-Moro |
Publisher | : World Scientific |
Total Pages | : 453 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 981279400X |
Download Advances in Algebraic Geometry Codes Book in PDF, ePub and Kindle
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.
Author | : Serguei A. Stepanov |
Publisher | : Springer Science & Business Media |
Total Pages | : 352 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461547857 |
Download Codes on Algebraic Curves Book in PDF, ePub and Kindle
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.
Author | : M. Tsfasman |
Publisher | : Springer Science & Business Media |
Total Pages | : 671 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 9401138109 |
Download Algebraic-Geometric Codes Book in PDF, ePub and Kindle
'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.
Author | : Carlos Moreno |
Publisher | : Cambridge University Press |
Total Pages | : 264 |
Release | : 1993-10-14 |
Genre | : Mathematics |
ISBN | : 9780521459013 |
Download Algebraic Curves Over Finite Fields Book in PDF, ePub and Kindle
Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.
Author | : Judy L. Walker |
Publisher | : American Mathematical Soc. |
Total Pages | : 82 |
Release | : 2000 |
Genre | : Computers |
ISBN | : 082182628X |
Download Codes and Curves Book in PDF, ePub and Kindle
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.
Author | : Vera Pless |
Publisher | : North Holland |
Total Pages | : 1220 |
Release | : 1998-11-16 |
Genre | : Computers |
ISBN | : |
Download Handbook of Coding Theory Book in PDF, ePub and Kindle
Author | : Michael Tsfasman |
Publisher | : American Mathematical Soc. |
Total Pages | : 453 |
Release | : 2019-07-02 |
Genre | : Coding theory |
ISBN | : 1470448653 |
Download Algebraic Geometry Codes: Advanced Chapters Book in PDF, ePub and Kindle
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.
Author | : Henning Stichtenoth |
Publisher | : Springer Science & Business Media |
Total Pages | : 360 |
Release | : 2009-02-11 |
Genre | : Mathematics |
ISBN | : 3540768785 |
Download Algebraic Function Fields and Codes Book in PDF, ePub and Kindle
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.