A Course In Algebraic Error Correcting Codes

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A Course in Algebraic Error-Correcting Codes

Author : Simeon Ball
Publisher : Springer Nature
ISBN 13 : 3030411532
Total Pages : 185 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis A Course in Algebraic Error-Correcting Codes by : Simeon Ball

Download or read book A Course in Algebraic Error-Correcting Codes written by Simeon Ball and published by Springer Nature. This book was released on 2020-05-08 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Simeon Michael Ball
Publisher :
ISBN 13 : 9783030411541
Total Pages : 0 pages
Book Rating : 4.4/5 (115 download)

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Book Synopsis A Course in Algebraic Error-Correcting Codes by : Simeon Michael Ball

Download or read book A Course in Algebraic Error-Correcting Codes written by Simeon Michael Ball and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Algorithms and Error-Correcting Codes

Author : Jaques Calmet
Publisher : Springer Science & Business Media
ISBN 13 : 9783540167761
Total Pages : 430 pages
Book Rating : 4.1/5 (677 download)

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Book Synopsis Algebraic Algorithms and Error-Correcting Codes by : Jaques Calmet

Download or read book Algebraic Algorithms and Error-Correcting Codes written by Jaques Calmet and published by Springer Science & Business Media. This book was released on 1986-07 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Error-Correcting Linear Codes

Author : Anton Betten
Publisher : Springer Science & Business Media
ISBN 13 : 3540317031
Total Pages : 819 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Error-Correcting Linear Codes by : Anton Betten

Download or read book Error-Correcting Linear Codes written by Anton Betten and published by Springer Science & Business Media. This book was released on 2006-09-21 with total page 819 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Course in Error-correcting Codes

Author : Jørn Justesen
Publisher : European Mathematical Society
ISBN 13 : 9783037190012
Total Pages : 210 pages
Book Rating : 4.1/5 (9 download)

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Book Synopsis A Course in Error-correcting Codes by : Jørn Justesen

Download or read book A Course in Error-correcting Codes written by Jørn Justesen and published by European Mathematical Society. This book was released on 2004 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Error-correcting Codes

Author : Mary Lay Stephenson
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (995 download)

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Book Synopsis Algebraic Error-correcting Codes by : Mary Lay Stephenson

Download or read book Algebraic Error-correcting Codes written by Mary Lay Stephenson and published by . This book was released on 1982 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A First Course in Coding Theory

Author : Raymond Hill
Publisher : Oxford University Press
ISBN 13 : 9780198538035
Total Pages : 268 pages
Book Rating : 4.5/5 (38 download)

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Book Synopsis A First Course in Coding Theory by : Raymond Hill

Download or read book A First Course in Coding Theory written by Raymond Hill and published by Oxford University Press. This book was released on 1986 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : D J. Baylis
Publisher : Routledge
ISBN 13 : 1351449834
Total Pages : 238 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Error Correcting Codes by : D J. Baylis

Download or read book Error Correcting Codes written by D J. Baylis and published by Routledge. This book was released on 2018-05-11 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fundamentals of Error-Correcting Codes

Author : W. Cary Huffman
Publisher : Cambridge University Press
ISBN 13 : 1139439502
Total Pages : 668 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Fundamentals of Error-Correcting Codes by : W. Cary Huffman

Download or read book Fundamentals of Error-Correcting Codes written by W. Cary Huffman and published by Cambridge University Press. This book was released on 2010-02-18 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Error-correcting Codes and Finite Fields

Author : Oliver Pretzel
Publisher : Oxford University Press on Demand
ISBN 13 : 9780192690678
Total Pages : 341 pages
Book Rating : 4.6/5 (96 download)

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Book Synopsis Error-correcting Codes and Finite Fields by : Oliver Pretzel

Download or read book Error-correcting Codes and Finite Fields written by Oliver Pretzel and published by Oxford University Press on Demand. This book was released on 1996 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra

Author : Thomas Beth
Publisher : Springer Science & Business Media
ISBN 13 : 9783540192008
Total Pages : 228 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra by : Thomas Beth

Download or read book Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra written by Thomas Beth and published by Springer Science & Business Media. This book was released on 1988-05-04 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 4th International Conference on Applicable Algebra, Error-Correcting Codes, Combinatorics and Computer Algebra (AAECC-4), held in Karlsruhe, 23-26 September, 1986. Selected papers which were given at the conference have been reviewed a second time and are presented here.

Error-correcting Codes and Finite Fields

Author : Oliver Pretzel
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Error-correcting Codes and Finite Fields by : Oliver Pretzel

Download or read book Error-correcting Codes and Finite Fields written by Oliver Pretzel and published by Oxford University Press, USA. This book was released on 1992 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the elementary ideas of parity check codes, this work takes the reader via BCH and Reed-Solomon codes all the way to the geometric Goppa codes. The necessary mathematics is developed in parallel with the applications.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Marc Fossorier
Publisher : Springer
ISBN 13 : 3540467963
Total Pages : 516 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Marc Fossorier

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Marc Fossorier and published by Springer. This book was released on 2003-07-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Teo Mora
Publisher : Springer Science & Business Media
ISBN 13 : 9783540631637
Total Pages : 372 pages
Book Rating : 4.6/5 (316 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Teo Mora

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Teo Mora and published by Springer Science & Business Media. This book was released on 1997-06-11 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Marc Fossorier
Publisher : Springer
ISBN 13 : 3540448284
Total Pages : 275 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Marc Fossorier

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Marc Fossorier and published by Springer. This book was released on 2003-08-03 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Serdar Boztas
Publisher : Springer
ISBN 13 : 3540456244
Total Pages : 411 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Serdar Boztas

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Serdar Boztas and published by Springer. This book was released on 2003-06-30 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The AAECC Symposia Series was started in 1983 by Alain Poli (Toulouse), who, together with R. Desq, D. Lazard, and P. Camion, organized the ?rst conference. Originally the acronym AAECC meant “Applied Algebra and Error-Correcting Codes”. Over the years its meaning has shifted to “Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes”, re?ecting the growing importance of complexity in both decoding algorithms and computational algebra. AAECC aims to encourage cross-fertilization between algebraic methods and their applications in computing and communications. The algebraic orientation is towards ?nite ?elds, complexity, polynomials, and graphs. The applications orientation is towards both theoretical and practical error-correction coding, and, since AAECC 13 (Hawaii, 1999), towards cryptography. AAECC was the ?rst symposium with papers connecting Gr ̈obner bases with E-C codes. The balance between theoretical and practical is intended to shift regularly; at AAECC-14 the focus was on the theoretical side. The main subjects covered were: – Codes: iterative decoding, decoding methods, block codes, code construction. – Codes and algebra: algebraic curves, Gr ̈obner bases, and AG codes. – Algebra: rings and ?elds, polynomials. – Codes and combinatorics: graphs and matrices, designs, arithmetic. – Cryptography. – Computational algebra: algebraic algorithms. – Sequences for communications.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Author : Serdar Boztas
Publisher : Springer Science & Business Media
ISBN 13 : 3540772235
Total Pages : 379 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Applied Algebra, Algebraic Algorithms and Error-Correcting Codes by : Serdar Boztas

Download or read book Applied Algebra, Algebraic Algorithms and Error-Correcting Codes written by Serdar Boztas and published by Springer Science & Business Media. This book was released on 2007-11-30 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007. The 33 revised full papers presented together with 8 invited papers were carefully reviewed and selected from 61 submissions. Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.