Error Correcting Linear Codes

Error Correcting Linear Codes

This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering.

Author: Anton Betten

Publisher: Springer Science & Business Media

ISBN: 9783540317036

Category: Mathematics

Page: 798

View: 782

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.
Categories: Mathematics

Error correcting Codes

Error correcting Codes

The coding problem; Introduction to algebra; Linear codes; Error correction capabilities of linear codes; Important linear block codes; Polynomial rings and galois fields; Linear switching circuits; Cyclic codes; Bose-chaudhuri-hocquenghem ...

Author: William Wesley Peterson

Publisher: MIT Press

ISBN: 0262160390

Category: Computers

Page: 560

View: 794

The coding problem; Introduction to algebra; Linear codes; Error correction capabilities of linear codes; Important linear block codes; Polynomial rings and galois fields; Linear switching circuits; Cyclic codes; Bose-chaudhuri-hocquenghem codes; Arithmetic codes.
Categories: Computers

Error Correcting Codes

Error Correcting Codes

Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical ...

Author: D J. Baylis

Publisher: Routledge

ISBN: 9781351449847

Category: Mathematics

Page: 232

View: 925

Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style.Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.
Categories: Mathematics

Fundamentals of Error Correcting Codes

Fundamentals of Error Correcting Codes

Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint.

Author: W. Cary Huffman

Publisher: Cambridge University Press

ISBN: 1139439502

Category: Technology & Engineering

Page:

View: 102

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.
Categories: Technology & Engineering

A Course in Algebraic Error Correcting Codes

A Course in Algebraic Error Correcting Codes

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.

Author: Simeon Ball

Publisher: Springer Nature

ISBN: 9783030411534

Category: Mathematics

Page: 177

View: 323

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.
Categories: Mathematics

An Introduction to Error Correcting Codes with Applications

An Introduction to Error Correcting Codes with Applications

5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 ...

Author: Scott A. Vanstone

Publisher: Springer Science & Business Media

ISBN: 9781475720327

Category: Technology & Engineering

Page: 289

View: 797

5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 Finite Fields and Factoring xn-l over GF(q) 181 5. 9 Another Method for Factoring xn-l over GF(q)t 187 5. 10 Exercises 193 Chapter 6 BCH Codes and Bounds for Cyclic Codes 6. 1 Introduction 201 6. 2 BCH Codes and the BCH Bound 205 6. 3 Bounds for Cyclic Codest 210 6. 4 Decoding BCH Codes 215 6. 5 Linearized Polynomials and Finding Roots of Polynomialst 224 6. 6 Exercises 231 Chapter 7 Error Correction Techniques and Digital Audio Recording 7. 1 Introduction 237 7. 2 Reed-Solomon Codes 237 7. 3 Channel Erasures 240 7. 4 BCH Decoding with Erasures 244 7. 5 Interleaving 250 7. 6 Error Correction and Digital Audio Recording 256 7.
Categories: Technology & Engineering

Error correcting Codes and Finite Fields

Error correcting Codes and Finite Fields

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.

Author: Oliver Pretzel

Publisher: Oxford University Press on Demand

ISBN: 0192690671

Category: Computers

Page: 341

View: 221

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.
Categories: Computers

Introduction to Coding Theory

Introduction to Coding Theory

This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

Author: Ron Roth

Publisher: Cambridge University Press

ISBN: 0521845041

Category: Computers

Page: 566

View: 128

This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.
Categories: Computers

An Introduction to Error correcting Codes

An Introduction to Error correcting Codes

Codes, Kodierung (Telegrafie) ; Kodierung, Datendarstellung, Bit, Byte (EDV).

Author: Shu Lin

Publisher: Prentice Hall

ISBN: UOM:39076006526870

Category: Codes correcteurs d'erreurs (Théorie de l'information)

Page: 330

View: 719

Codes, Kodierung (Telegrafie) ; Kodierung, Datendarstellung, Bit, Byte (EDV).
Categories: Codes correcteurs d'erreurs (Théorie de l'information)

A Course in Error correcting Codes

A Course in Error correcting Codes

This book is written as a text for a course aimed at advanced undergraduates.

Author: Jørn Justesen

Publisher: European Mathematical Society

ISBN: 3037190019

Category: Error-correcting codes (Information theory)

Page: 194

View: 676

This book is written as a text for a course aimed at advanced undergraduates. Chapters cover the codes and decoding methods that are currently of most interest in research, development, and application. They give a relatively brief presentation of the essential results, emphasizing the interrelations between different methods and proofs of all important results. A sequence of problems at the end of each chapter serves to review the results and give the student an appreciation of the concepts.
Categories: Error-correcting codes (Information theory)

Introduction to the Theory of Error correcting Codes

Introduction to the Theory of Error correcting Codes

An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book.

Author: Vera Pless

Publisher: Wiley-Interscience

ISBN: UOM:39015015706206

Category: Error-correcting codes (Information theory).

Page: 201

View: 603

An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book. It considers such codes as Hamming codes and Golay codes, correction of double errors, use of finite fields, cyclic codes, BCH codes and weight distributions, as well as design of codes. In this second edition, the author includes more material on non-binary code and cyclic codes. In addition some proofs have been simplified and there are many more examples and problems. The text has been aimed at mathematicians, electrical engineers and computer scientists.
Categories: Error-correcting codes (Information theory).

Coding Theory

Coding Theory

Modern introduction to theory of coding and decoding with many exercises and examples.

Author: San Ling

Publisher: Cambridge University Press

ISBN: 0521529239

Category: Mathematics

Page: 222

View: 470

Modern introduction to theory of coding and decoding with many exercises and examples.
Categories: Mathematics

Error correcting Codes Finite Geometries and Cryptography

Error correcting Codes  Finite Geometries  and Cryptography

Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.

Author: Aiden A. Bruen

Publisher: American Mathematical Soc.

ISBN: 9780821849569

Category: Mathematics

Page: 244

View: 104

This interdisciplinary volume contains papers from both a conference and special session on Error-Control Codes, Information Theory and Applied Cryptography. The conference was held at the Fields Institute in Toronto, On, Canada from December 5-6, 2007, and the special session was held at the Canadian Mathematical Society's winter meeting in London, ON, Canada from December 8-10, 2007. The volume features cutting-edge theoretical results on the Reed-Muller and Reed-Solomon codes, classical linear codes, codes from nets and block designs, LDPC codes, perfect quantum and orthogonal codes, iterative decoding, magnetic storage and digital memory devices, and MIMO channels. There are new contributions on privacy reconciliation, resilient functions, cryptographic hash functions, and new work on quantum coins. Related original work in finite geometries concerns two-weight codes coming from partial spreads, (0, 1) matrices with forbidden configurations, Andre embeddings, and representations of projective spaces in affine planes. Great care has been taken to ensure that high expository standards are met by the papers in this volume. Accordingly, the papers are written in a user-friendly format. The hope is that this volume will be of interst and of benefit both to the experienced and to newcomers alike.
Categories: Mathematics

A First Course in Coding Theory

A First Course in Coding Theory

This book provides and elementary, yet rigorous, introduction to the theory of error-correcting codes.

Author: Raymond Hill

Publisher: Oxford University Press

ISBN: 0198538030

Category: Mathematics

Page: 251

View: 758

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.
Categories: Mathematics

A Practical Guide to Error Control Coding Using MATLAB

A Practical Guide to Error Control Coding Using MATLAB

This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes.You find clear guidance on code construction, decoding algorithms, and error correcting performances.

Author: Yuan Jiang

Publisher: Artech House

ISBN: 9781608070893

Category: Computer programming

Page: 292

View: 254

This practical resource provides you with a comprehensive understanding of error control coding, an essential and widely applied area in modern digital communications. The goal of error control coding is to encode information in such a way that even if the channel (or storage medium) introduces errors, the receiver can correct the errors and recover the original transmitted information. This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes.You find clear guidance on code construction, decoding algorithms, and error correcting performances. Moreover, this unique book introduces computer simulations integrally to help you master key concepts. Including a companion DVD with MATLAB programs and supported with over 540 equations, this hands-on reference provides you with an in-depth treatment of a wide range of practical implementation issues.
Categories: Computer programming

A Commonsense Approach to the Theory of Error Correcting Codes

A Commonsense Approach to the Theory of Error Correcting Codes

This text explains the basic circuits in a refreshingly practical way thatwill appeal to undergraduate electrical engineering students as well as to engineers and techniciansworking in industry.Arazi's truly commonsense approach provides a ...

Author: Benjamin Arazi

Publisher: MIT Press

ISBN: 0262010984

Category: Computers

Page: 208

View: 841

Teaching the theory of error correcting codes on an introductory level is a difficulttask. The theory, which has immediate hardware applications, also concerns highly abstractmathematical concepts. This text explains the basic circuits in a refreshingly practical way thatwill appeal to undergraduate electrical engineering students as well as to engineers and techniciansworking in industry.Arazi's truly commonsense approach provides a solid grounding in the subject,explaining principles intuitively from a hardware perspective. He fully covers error correctiontechniques, from basic parity check and single error correction cyclic codes to burst errorcorrecting codes and convolutional codes. All this he presents before introducing Galois fieldtheory - the basic algebraic treatment and theoretical basis of the subject, which usually appearsin the opening chapters of standard textbooks. One entire chapter is devoted to specific practicalissues, such as Reed-Solomon codes (used in compact disc equipment), and maximum length sequences(used in various fields of communications). The basic circuits explained throughout the book areredrawn and analyzed from a theoretical point of view for readers who are interested in tackling themathematics at a more advanced level.Benjamin Arazi is an Associate Professor in the Department ofElectrical and Computer Engineering at the Ben-Gurion University of the Negev. His book is includedin the Computer Systems Series, edited by Herb Schwetman.
Categories: Computers

Error Correcting Codes

Error Correcting Codes

Author: University of Wisconsin--Madison. Mathematics Research Center

Publisher:

ISBN: UOM:39015002075367

Category: Error-correcting codes (Information theory)

Page: 231

View: 154

Categories: Error-correcting codes (Information theory)