A Course In Algebraic Error Correcting Codes
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Author | : Simeon Ball |
Publisher | : Springer Nature |
Total Pages | : 185 |
Release | : 2020-05-08 |
Genre | : Mathematics |
ISBN | : 3030411532 |
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.
Author | : Simeon Michael Ball |
Publisher | : |
Total Pages | : 0 |
Release | : 2020 |
Genre | : Coding theory |
ISBN | : 9783030411541 |
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.
Author | : Jaques Calmet |
Publisher | : Springer Science & Business Media |
Total Pages | : 430 |
Release | : 1986-07 |
Genre | : Computers |
ISBN | : 9783540167761 |
Author | : Anton Betten |
Publisher | : Springer Science & Business Media |
Total Pages | : 819 |
Release | : 2006-09-21 |
Genre | : Mathematics |
ISBN | : 3540317031 |
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.
Author | : Jørn Justesen |
Publisher | : European Mathematical Society |
Total Pages | : 210 |
Release | : 2004 |
Genre | : Error-correcting codes (Information theory) |
ISBN | : 9783037190012 |
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.
Author | : Mary Lay Stephenson |
Publisher | : |
Total Pages | : 86 |
Release | : 1982 |
Genre | : Error-correcting codes (Information theory) |
ISBN | : |
Author | : Raymond Hill |
Publisher | : Oxford University Press |
Total Pages | : 268 |
Release | : 1986 |
Genre | : Computers |
ISBN | : 9780198538035 |
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.
Author | : D J. Baylis |
Publisher | : Routledge |
Total Pages | : 238 |
Release | : 2018-05-11 |
Genre | : Mathematics |
ISBN | : 1351449834 |
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.
Author | : W. Cary Huffman |
Publisher | : Cambridge University Press |
Total Pages | : 668 |
Release | : 2010-02-18 |
Genre | : Technology & Engineering |
ISBN | : 1139439502 |
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.
Author | : Oliver Pretzel |
Publisher | : Oxford University Press on Demand |
Total Pages | : 341 |
Release | : 1996 |
Genre | : Computers |
ISBN | : 9780192690678 |
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.