Algebraic Geometry Codes: Advanced Chapters - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry Codes: Advanced Chapters write by Michael Tsfasman. This book was released on 2019-07-02. Algebraic Geometry Codes: Advanced Chapters available 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.
Algebraic Geometric Codes: Basic Notions
Algebraic Geometric Codes: Basic Notions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometric Codes: Basic Notions write by Michael Tsfasman. This book was released on 2022-04-15. Algebraic Geometric Codes: Basic Notions available in PDF, EPUB and Kindle. 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.
Algebraic-Geometric Codes
Algebraic-Geometric Codes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic-Geometric Codes write by M. Tsfasman. This book was released on 2013-12-01. Algebraic-Geometric Codes available 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.
Advances in Algebraic Geometry Codes
Advances in Algebraic Geometry Codes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Algebraic Geometry Codes write by Edgar Martinez-Moro. This book was released on 2008. Advances in Algebraic Geometry Codes available 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.
Algebraic Geometry in Coding Theory and Cryptography
Algebraic Geometry in Coding Theory and Cryptography - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry in Coding Theory and Cryptography write by Harald Niederreiter. This book was released on 2009-09-21. Algebraic Geometry in Coding Theory and Cryptography available in PDF, EPUB and Kindle. 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
