Algebraic And Stochastic Coding Theory

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Algebraic and Stochastic Coding Theory

Author : Dave K. Kythe
Publisher : CRC Press
ISBN 13 : 135183245X
Total Pages : 515 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Algebraic and Stochastic Coding Theory by : Dave K. Kythe

Download or read book Algebraic and Stochastic Coding Theory written by Dave K. Kythe and published by CRC Press. This book was released on 2017-07-28 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.

Concise Encyclopedia of Coding Theory

Author : W. Cary Huffman
Publisher : CRC Press
ISBN 13 : 1351375105
Total Pages : 998 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Concise Encyclopedia of Coding Theory by : W. Cary Huffman

Download or read book Concise Encyclopedia of Coding Theory written by W. Cary Huffman and published by CRC Press. This book was released on 2021-03-26 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research

Introduction to Coding Theory and Algebraic Geometry

Author : J. van Lint
Publisher : Birkhäuser
ISBN 13 : 3034892861
Total Pages : 82 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Introduction to Coding Theory and Algebraic Geometry by : J. van Lint

Download or read book Introduction to Coding Theory and Algebraic Geometry written by J. van Lint and published by Birkhäuser. This book was released on 2012-12-06 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Stochastic Coding Theory

Author : Dave K. Kythe
Publisher : CRC Press
ISBN 13 : 1466505621
Total Pages : 507 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Algebraic and Stochastic Coding Theory by : Dave K. Kythe

Download or read book Algebraic and Stochastic Coding Theory written by Dave K. Kythe and published by CRC Press. This book was released on 2017-07-28 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes. It then examines codes based on the Galois field theory as well as their application in BCH and especially the Reed–Solomon codes that have been used for error correction of data transmissions in space missions. The major outlook in coding theory seems to be geared toward stochastic processes, and this book takes a bold step in this direction. As research focuses on error correction and recovery of erasures, the book discusses belief propagation and distributions. It examines the low-density parity-check and erasure codes that have opened up new approaches to improve wide-area network data transmission. It also describes modern codes, such as the Luby transform and Raptor codes, that are enabling new directions in high-speed transmission of very large data to multiple users. This robust, self-contained text fully explains coding problems, illustrating them with more than 200 examples. Combining theory and computational techniques, it will appeal not only to students but also to industry professionals, researchers, and academics in areas such as coding theory and signal and image processing.

Topics in Geometry, Coding Theory and Cryptography

Author : Arnaldo Garcia
Publisher : Springer Science & Business Media
ISBN 13 : 1402053347
Total Pages : 212 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Topics in Geometry, Coding Theory and Cryptography by : Arnaldo Garcia

Download or read book Topics in Geometry, Coding Theory and Cryptography written by Arnaldo Garcia and published by Springer Science & Business Media. This book was released on 2006-11-15 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.

Introduction to Coding Theory

Author : J.H. van Lint
Publisher : Springer Science & Business Media
ISBN 13 : 3642585752
Total Pages : 244 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Introduction to Coding Theory by : J.H. van Lint

Download or read book Introduction to Coding Theory written by J.H. van Lint and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction, the chapter requires more mathematical background of the reader than the remainder of this book. One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 7l.4• There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10.

Algebraic Coding Theory and Applications

Author : Carlos R. P. Hartmann
Publisher :
ISBN 13 : 9783662396421
Total Pages : 548 pages
Book Rating : 4.3/5 (964 download)

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Book Synopsis Algebraic Coding Theory and Applications by : Carlos R. P. Hartmann

Download or read book Algebraic Coding Theory and Applications written by Carlos R. P. Hartmann and published by . This book was released on 2014-09-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Coding Theory

Author : Jurgen Bierbrauer
Publisher : CRC Press
ISBN 13 : 148229981X
Total Pages : 512 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction to Coding Theory by : Jurgen Bierbrauer

Download or read book Introduction to Coding Theory written by Jurgen Bierbrauer and published by CRC Press. This book was released on 2016-10-14 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed to be usable as a textbook for an undergraduate course or for an advanced graduate course in coding theory as well as a reference for researchers in discrete mathematics, engineering and theoretical computer science. This second edition has three parts: an elementary introduction to coding, theory and applications of codes, and algebraic curves. The latter part presents a brief introduction to the theory of algebraic curves and its most important applications to coding theory.

Algebraic coding theory

Author : Elwyn R. Berlekamp
Publisher :
ISBN 13 :
Total Pages : 466 pages
Book Rating : 4.:/5 (833 download)

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Book Synopsis Algebraic coding theory by : Elwyn R. Berlekamp

Download or read book Algebraic coding theory written by Elwyn R. Berlekamp and published by . This book was released on 1961 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Information and Coding Theory

Author : Gareth A. Jones
Publisher : Springer Science & Business Media
ISBN 13 : 9781852336226
Total Pages : 228 pages
Book Rating : 4.3/5 (362 download)

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Book Synopsis Information and Coding Theory by : Gareth A. Jones

Download or read book Information and Coding Theory written by Gareth A. Jones and published by Springer Science & Business Media. This book was released on 2000-06-26 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an elementary introduction to information and coding theory. The first part focuses on information theory, covering uniquely decodable and instantaneous codes, Huffman coding, entropy, information channels, and Shannon’s Fundamental Theorem. In the second part, linear algebra is used to construct examples of such codes, such as the Hamming, Hadamard, Golay and Reed-Muller codes. Contains proofs, worked examples, and exercises.

Coding Theory

Author : Jacobus H. van Lint
Publisher : Springer
ISBN 13 : 3662207125
Total Pages : 145 pages
Book Rating : 4.6/5 (622 download)

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Book Synopsis Coding Theory by : Jacobus H. van Lint

Download or read book Coding Theory written by Jacobus H. van Lint and published by Springer. This book was released on 2013-12-11 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Algebraic and Combinatorial Coding Theory

Author : Ian F. Blake
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis An Introduction to Algebraic and Combinatorial Coding Theory by : Ian F. Blake

Download or read book An Introduction to Algebraic and Combinatorial Coding Theory written by Ian F. Blake and published by . This book was released on 1976 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Geometric Codes: Basic Notions

Author : Michael Tsfasman
Publisher : American Mathematical Society
ISBN 13 : 1470470071
Total Pages : 338 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebraic Geometric Codes: Basic Notions by : Michael Tsfasman

Download or read book Algebraic Geometric Codes: Basic Notions written by Michael Tsfasman and published by American Mathematical Society. This book was released on 2022-04-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Geometry for Coding Theory and Cryptography

Author : Everett W. Howe
Publisher : Springer
ISBN 13 : 3319639315
Total Pages : 160 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Algebraic Geometry for Coding Theory and Cryptography by : Everett W. Howe

Download or read book Algebraic Geometry for Coding Theory and Cryptography written by Everett W. Howe and published by Springer. This book was released on 2017-11-15 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Coding Theory and Algebraic Geometry

Author : Henning Stichtenoth
Publisher :
ISBN 13 : 9783662174821
Total Pages : 240 pages
Book Rating : 4.1/5 (748 download)

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Book Synopsis Coding Theory and Algebraic Geometry by : Henning Stichtenoth

Download or read book Coding Theory and Algebraic Geometry written by Henning Stichtenoth and published by . This book was released on 2014-01-15 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lattices and Codes

Author : Wolfgang Ebeling
Publisher : Springer Science & Business Media
ISBN 13 : 3658003596
Total Pages : 177 pages
Book Rating : 4.6/5 (58 download)

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Book Synopsis Lattices and Codes by : Wolfgang Ebeling

Download or read book Lattices and Codes written by Wolfgang Ebeling and published by Springer Science & Business Media. This book was released on 2013 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory. In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated. Content Lattices and Codes -Theta Functions and Weight Enumerators - Even Unimodular Lattices - The Leech Lattice - Lattices over Integers of Number Fields and Self-Dual Codes. Readership Graduate Students in Mathematics and Computer Science Mathematicians and Computer Scientists About the Author Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany

Algebraic Codes on Lines, Planes, and Curves

Author : Richard E. Blahut
Publisher : Cambridge University Press
ISBN 13 : 1139469460
Total Pages : 10 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Algebraic Codes on Lines, Planes, and Curves by : Richard E. Blahut

Download or read book Algebraic Codes on Lines, Planes, and Curves written by Richard E. Blahut and published by Cambridge University Press. This book was released on 2008-04-03 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.