Coding Theory And Algebraic Geometry
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Coding Theory And Algebraic Geometry
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Author : Henning Stichtenoth
language : en
Publisher: Springer
Release Date : 2006-11-15
Coding Theory And Algebraic Geometry written by Henning Stichtenoth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Introduction To Coding Theory And Algebraic Geometry
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Author : J. van Lint
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Introduction To Coding Theory And Algebraic Geometry written by J. van Lint and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
These notes are based on lectures given in the semmar on "Coding Theory and Algebraic Geometry" held at Schloss Mickeln, Diisseldorf, November 16-21, 1987. In 1982 Tsfasman, Vladut and Zink, using algebraic geometry and ideas of Goppa, constructed a seqeunce of codes that exceed the Gilbert-Varshamov bound. The result was considered sensational. Furthermore, it was surprising to see these unrelated areas of mathematics collaborating. The aim of this course is to give an introduction to coding theory and to sketch the ideas of algebraic geometry that led to the new result. Finally, a number of applications of these methods of algebraic geometry to coding theory are given. Since this is a new area, there are presently no references where one can find a more extensive treatment of all the material. However, both for algebraic geometry and for coding theory excellent textbooks are available. The combination ofthe two subjects can only be found in a number ofsurvey papers. A book by C. Moreno with a complete treatment of this area is in preparation. We hope that these notes will stimulate further research and collaboration of algebraic geometers and coding theorists. G. van der Geer, J.H. van Lint Introduction to CodingTheory and Algebraic Geometry PartI -- CodingTheory Jacobus H. vanLint 11 1. Finite fields In this chapter we collect (without proof) the facts from the theory of finite fields that we shall need in this course
Algebraic Geometric Codes Basic Notions
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Author : Michael Tsfasman
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-15
Algebraic Geometric Codes Basic Notions written by Michael Tsfasman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-15 with Mathematics categories.
The book is devoted to the theory of algebraic geometric codes, a subject formed on the border of several domains of mathematics. On one side there are such classical areas as algebraic geometry and number theory; on the other, information transmission theory, combinatorics, finite geometries, dense packings, etc. The authors give a unique perspective on the subject. Whereas most books on coding theory build up coding theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, this book constantly looks for interpretations that connect coding theory to algebraic geometry and number theory. There are no prerequisites other than a standard algebra graduate course. The first two chapters of the book can serve as an introduction to coding theory and algebraic geometry respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the last chapter the authors explain relations between all of these: the theory of algebraic geometric codes.
Coding Theory And Algebraic Geometry
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Author : Henning Stichtenoth
language : en
Publisher:
Release Date : 2014-01-15
Coding Theory And Algebraic Geometry written by Henning Stichtenoth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Algebraic Geometry In Coding Theory And Cryptography
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Author : Harald Niederreiter
language : en
Publisher: Princeton University Press
Release Date : 2009-09-21
Algebraic Geometry In Coding Theory And Cryptography written by Harald Niederreiter 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 2009-09-21 with Mathematics categories.
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
Introduction To Coding Theory And Algebraic Geometry
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Author : Jacobus Hendricus van Lint
language : en
Publisher: Birkhauser
Release Date : 1988
Introduction To Coding Theory And Algebraic Geometry written by Jacobus Hendricus van Lint and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Codage (Informatique) categories.
Algebraic Geometry Modeling In Information Theory
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Author : Edgar Martinez-Moro
language : en
Publisher: World Scientific
Release Date : 2013
Algebraic Geometry Modeling In Information Theory 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 2013 with Computers categories.
Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.
Introduction To Algebraic Coding Theory
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Author : Tzuong-tsieng Moh
language : en
Publisher: World Scientific
Release Date : 2022-02-18
Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Mathematics categories.
In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.
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.
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 Coding theory 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.