Algebraic Coding Theory (Revised Edition)
Algebraic Coding Theory (Revised Edition)

Author: Elwyn R Berlekamp

Publisher: World Scientific

Published: 2015-03-26

Total Pages: 501

ISBN-13: 981463591X

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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.

The Mathematical Theory of Coding
The Mathematical Theory of Coding

Author: Ian F. Blake

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 369

ISBN-13: 1483260593

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The Mathematical Theory of Coding focuses on the application of algebraic and combinatoric methods to the coding theory, including linear transformations, vector spaces, and combinatorics. The publication first offers information on finite fields and coding theory and combinatorial constructions and coding. Discussions focus on self-dual and quasicyclic codes, quadratic residues and codes, balanced incomplete block designs and codes, bounds on code dictionaries, code invariance under permutation groups, and linear transformations of vector spaces over finite fields. The text then takes a look at coding and combinatorics and the structure of semisimple rings. Topics include structure of cyclic codes and semisimple rings, group algebra and group characters, rings, ideals, and the minimum condition, chains and chain groups, dual chain groups, and matroids, graphs, and coding. The book ponders on group representations and group codes for the Gaussian channel, including distance properties of group codes, initial vector problem, modules, group algebras, andrepresentations, orthogonality relationships and properties of group characters, and representation of groups. The manuscript is a valuable source of data for mathematicians and researchers interested in the mathematical theory of coding.

Selected Topics In Information And Coding Theory
Selected Topics In Information And Coding Theory

Author: Isaac Woungang

Publisher: World Scientific

Published: 2010-02-26

Total Pages: 725

ISBN-13: 981446919X

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The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.

Advances In Algebraic Geometry Codes
Advances In Algebraic Geometry Codes

Author: Edgar Martinez-moro

Publisher: World Scientific

Published: 2008-10-08

Total Pages: 453

ISBN-13: 9814471615

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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.

Network Coding Theory
Network Coding Theory

Author: Raymond W. Yeung

Publisher: Now Publishers Inc

Published: 2006

Total Pages: 156

ISBN-13: 1933019247

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Provides a tutorial on the basics of network coding theory. Divided into two parts, this book presents a unified framework for understanding the basic notions and fundamental results in network coding. It is aimed at students, researchers and practitioners working in networking research.

Poset Codes: Partial Orders, Metrics and Coding Theory
Poset Codes: Partial Orders, Metrics and Coding Theory

Author: Marcelo Firer

Publisher: Springer

Published: 2018-11-01

Total Pages: 133

ISBN-13: 3319938215

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This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, were first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards coding theory for poset metrics and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven results. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.

Introduction To Algebraic Coding Theory
Introduction To Algebraic Coding Theory

Author: Tzuong-tsieng Moh

Publisher: World Scientific

Published: 2022-02-18

Total Pages: 266

ISBN-13: 9811220980

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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.