A Course In Algebraic Error Correcting Codes
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Author |
: Simeon Ball |
Publisher |
: Springer Nature |
Total Pages |
: 185 |
Release |
: 2020-05-08 |
ISBN-10 |
: 9783030411534 |
ISBN-13 |
: 3030411532 |
Rating |
: 4/5 (34 Downloads) |
Synopsis A Course in Algebraic Error-Correcting Codes by : Simeon Ball
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 |
ISBN-10 |
: 3030411540 |
ISBN-13 |
: 9783030411541 |
Rating |
: 4/5 (40 Downloads) |
Synopsis A Course in Algebraic Error-Correcting Codes by : Simeon Michael Ball
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 |
ISBN-10 |
: 3540167765 |
ISBN-13 |
: 9783540167761 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Algebraic Algorithms and Error-Correcting Codes by : Jaques Calmet
Author |
: Anton Betten |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 819 |
Release |
: 2006-09-21 |
ISBN-10 |
: 9783540317036 |
ISBN-13 |
: 3540317031 |
Rating |
: 4/5 (36 Downloads) |
Synopsis Error-Correcting Linear Codes by : Anton Betten
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 |
: D J. Baylis |
Publisher |
: Routledge |
Total Pages |
: 238 |
Release |
: 2018-05-11 |
ISBN-10 |
: 9781351449830 |
ISBN-13 |
: 1351449834 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Error Correcting Codes by : D J. Baylis
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 |
: Jørn Justesen |
Publisher |
: European Mathematical Society |
Total Pages |
: 210 |
Release |
: 2004 |
ISBN-10 |
: 3037190019 |
ISBN-13 |
: 9783037190012 |
Rating |
: 4/5 (19 Downloads) |
Synopsis A Course in Error-correcting Codes by : Jørn Justesen
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 |
ISBN-10 |
: OCLC:9953366 |
ISBN-13 |
: |
Rating |
: 4/5 (66 Downloads) |
Synopsis Algebraic Error-correcting Codes by : Mary Lay Stephenson
Author |
: Raymond Hill |
Publisher |
: Oxford University Press |
Total Pages |
: 268 |
Release |
: 1986 |
ISBN-10 |
: 0198538030 |
ISBN-13 |
: 9780198538035 |
Rating |
: 4/5 (30 Downloads) |
Synopsis A First Course in Coding Theory by : Raymond Hill
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 |
: Marc Fossorier |
Publisher |
: Springer |
Total Pages |
: 275 |
Release |
: 2003-08-03 |
ISBN-10 |
: 9783540448280 |
ISBN-13 |
: 3540448284 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Marc Fossorier
This book constitutes the refereed proceedings of the 15th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-15, held in Toulouse, France, in May 2003.The 25 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 40 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.
Author |
: Teo Mora |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 372 |
Release |
: 1997-06-11 |
ISBN-10 |
: 3540631631 |
ISBN-13 |
: 9783540631637 |
Rating |
: 4/5 (31 Downloads) |
Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Teo Mora
This book constitutes the strictly refereed proceedings of the 12th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-12, held in Toulouse, France, June 1997. The 27 revised full papers presented were carefully selected by the program committee for inclusion in the volume. The papers address a broad range of current issues in coding theory and computer algebra spanning polynomials, factorization, commutative algebra, real geometry, group theory, etc. on the mathematical side as well as software systems, telecommunication, complexity theory, compression, signal processing, etc. on the computer science and engineering side.