A Course in Algebraic Error-Correcting Codes

A Course in Algebraic Error-Correcting Codes PDF Author: Simeon Ball
Publisher: Springer Nature
ISBN: 3030411532
Category : Mathematics
Languages : en
Pages : 185

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Book Description
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

A Course in Algebraic Error-Correcting Codes

A Course in Algebraic Error-Correcting Codes PDF Author: Simeon Ball
Publisher: Springer Nature
ISBN: 3030411532
Category : Mathematics
Languages : en
Pages : 185

Get Book Here

Book Description
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

A Course in Algebraic Error-Correcting Codes

A Course in Algebraic Error-Correcting Codes PDF Author: Simeon Michael Ball
Publisher:
ISBN: 9783030411541
Category : Coding theory
Languages : en
Pages : 0

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Book Description
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes. Early chapters cover fundamental concepts, introducing Shannon's theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions. A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.

Error-Correcting Linear Codes

Error-Correcting Linear Codes PDF Author: Anton Betten
Publisher: Springer Science & Business Media
ISBN: 3540317031
Category : Mathematics
Languages : en
Pages : 819

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Book Description
This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

A First Course in Coding Theory

A First Course in Coding Theory PDF Author: Raymond Hill
Publisher: Oxford University Press
ISBN: 9780198538035
Category : Computers
Languages : en
Pages : 268

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Book Description
Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

Error-correcting Codes and Finite Fields

Error-correcting Codes and Finite Fields PDF Author: Oliver Pretzel
Publisher: Oxford University Press on Demand
ISBN: 9780192690678
Category : Computers
Languages : en
Pages : 341

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Book Description
This textbook is a reprint of Chapters 1-20 of the original hardback edition. It provides the reader with the tools necessary to implement modern error-processing schemes. The material on algebraic geometry and geometric Goppa codes, which is not part of a standard introductory course on coding theory, has been omitted. The book assumes only a basic knowledge of linear algebra and develops the mathematical theory in parallel with the codes. Central to the text are worked examples whichmotivate and explain the theory. The book is in four parts. The first introduces the basic ideas of coding theory. The second and third cover the theory of finite fields and give a detailed treatment of BCH and Reed-Solomon codes. These parts are linked by their uses of Eulid's algorithm as a central technique. The fourth part treats classical Goppa codes.

Algebraic Coding Theory (Revised Edition)

Algebraic Coding Theory (Revised Edition) PDF Author: Elwyn R Berlekamp
Publisher: World Scientific
ISBN: 981463591X
Category : Mathematics
Languages : en
Pages : 501

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Book Description
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.

Fundamentals of Error-Correcting Codes

Fundamentals of Error-Correcting Codes PDF Author: W. Cary Huffman
Publisher: Cambridge University Press
ISBN: 1139439502
Category : Technology & Engineering
Languages : en
Pages : 668

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Book Description
Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, there is much coverage of techniques which could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering or computer science background.

Fundamentals of Classical and Modern Error-Correcting Codes

Fundamentals of Classical and Modern Error-Correcting Codes PDF Author: Shu Lin
Publisher: Cambridge University Press
ISBN: 1316512622
Category : Computers
Languages : en
Pages : 843

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Book Description
An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.

Coding Theory

Coding Theory PDF Author: Jacobus H. van Lint
Publisher: Springer
ISBN: 3662207125
Category : Mathematics
Languages : en
Pages : 145

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Book Description


Coding Theory

Coding Theory PDF Author: San Ling
Publisher: Cambridge University Press
ISBN: 9780521529235
Category : Computers
Languages : en
Pages : 238

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Book Description
Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.