Algebraic Coding Theory History And Development
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Algebraic Coding Theory History And Development
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Author : Ian F. Blake
language : en
Publisher:
Release Date : 1973
Algebraic Coding Theory History And Development written by Ian F. Blake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Computers categories.
Algebraic Coding Theory History And Development
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Author : Elwyn R. Berlekamp
language : en
Publisher:
Release Date : 1968
Algebraic Coding Theory History And Development written by Elwyn R. Berlekamp and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Coding theory categories.
Algebraic Coding Theory History And Development
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Author : Ian F. Blake
language : en
Publisher:
Release Date : 1973
Algebraic Coding Theory History And Development written by Ian F. Blake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Computers categories.
Algebraic And Stochastic Coding Theory
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Author : Dave K. Kythe
language : en
Publisher: CRC Press
Release Date : 2017-07-28
Algebraic And Stochastic Coding Theory written by Dave K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-28 with Computers categories.
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
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Author : W. Cary Huffman
language : en
Publisher: CRC Press
Release Date : 2021-03-25
Concise Encyclopedia Of Coding Theory written by W. Cary Huffman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-25 with Computers categories.
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
Algebraic Coding Theory Revised Edition
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Author : Elwyn R Berlekamp
language : en
Publisher: World Scientific
Release Date : 2015-03-26
Algebraic Coding Theory Revised Edition written by Elwyn R Berlekamp and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-26 with Mathematics categories.
This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
Information Theory And Coding By Example
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Author : Mark Kelbert
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-12
Information Theory And Coding By Example written by Mark Kelbert and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-12 with Computers categories.
A valuable teaching aid. Provides relevant background material, many examples and clear solutions to problems taken from real exam papers.
Applied Algebra Algebraic Algorithms And Error Correcting Codes
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Author : Gérard Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 1995
Applied Algebra Algebraic Algorithms And Error Correcting Codes written by Gérard Cohen 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 1995 with Algebra categories.
This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.
Codes Cryptology And Curves With Computer Algebra
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Author : Ruud Pellikaan
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-02
Codes Cryptology And Curves With Computer Algebra written by Ruud Pellikaan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-02 with Computers categories.
Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.
Applied Abstract Algebra
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Author : Rudolf Lidl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Abstract Algebra written by Rudolf Lidl 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.
There is at present a growing body of opinion that in the decades ahead discrete mathematics (that is, "noncontinuous mathematics"), and therefore parts of applicable modern algebra, will be of increasing importance. Cer tainly, one reason for this opinion is the rapid development of computer science, and the use of discrete mathematics as one of its major tools. The purpose of this book is to convey to graduate students or to final-year undergraduate students the fact that the abstract algebra encountered pre viously in a first algebra course can be used in many areas of applied mathematics. It is often the case that students who have studied mathematics go into postgraduate work without any knowledge of the applicability of the structures they have studied in an algebra course. In recent years there have emerged courses and texts on discrete mathe matics and applied algebra. The present text is meant to add to what is available, by focusing on three subject areas. The contents of this book can be described as dealing with the following major themes: Applications of Boolean algebras (Chapters 1 and 2). Applications of finite fields (Chapters 3 to 5). Applications of semigroups (Chapters 6 and 7).