Codes On Algebraic Curves
DOWNLOAD
Download Codes On Algebraic Curves PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Codes On Algebraic Curves book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Codes And Algebraic Curves
DOWNLOAD
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
DOWNLOAD
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.
Algebraic Geometric Codes
DOWNLOAD
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.
Advances In Algebraic Geometry Codes
DOWNLOAD
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 Codes Advanced Chapters
DOWNLOAD
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.
Codes And Curves
DOWNLOAD
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.
Algebraic Curves Over A Finite Field
DOWNLOAD
Author : J. W. P. Hirschfeld
language : en
Publisher: Princeton University Press
Release Date : 2013-03-25
Algebraic Curves Over A Finite Field written by J. W. P. Hirschfeld and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-25 with Mathematics categories.
This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Algebraic Geometry For Coding Theory And Cryptography
DOWNLOAD
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 Curves And Signals
DOWNLOAD
Author : Alexander Vardy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Codes Curves And Signals written by Alexander Vardy 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 Technology & Engineering categories.
Codes, Curves, and Signals: Common Threads in Communications is a collection of seventeen contributions from leading researchers in communications. The book provides a representative cross-section of cutting edge contemporary research in the fields of algebraic curves and the associated decoding algorithms, the use of signal processing techniques in coding theory, and the application of information-theoretic methods in communications and signal processing. The book is organized into three parts: Curves and Codes, Codes and Signals, and Signals and Information. Codes, Curves, and Signals: Common Threads in Communications is a tribute to the broad and profound influence of Richard E. Blahut on the fields of algebraic coding, information theory, and digital signal processing. All the contributors have individually and collectively dedicated their work to R. E. Blahut. Codes, Curves, and Signals: Common Threads in Communications is an excellent reference for researchers and professionals.
Constructing Codes From Algebraic Curves
DOWNLOAD
Author : Tyler R. Tennille
language : en
Publisher:
Release Date : 2002
Constructing Codes From Algebraic Curves written by Tyler R. Tennille and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Curves, Algebraic categories.