Error Correcting Codes And Finite Fields
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| 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.
| Author | : Florence Jessie MacWilliams |
| Publisher | : Elsevier |
| Total Pages | : 787 |
| Release | : 1977 |
| Genre | : Computers |
| ISBN | : 0444850104 |
| Author | : Oliver Pretzel |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 424 |
| Release | : 1992 |
| Genre | : Computers |
| ISBN | : |
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.
| 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 | : Scott A. Vanstone |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 297 |
| Release | : 2013-04-18 |
| Genre | : Technology & Engineering |
| ISBN | : 1475720327 |
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.
| 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 | : 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 | : 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 | : Vera Pless |
| Publisher | : John Wiley & Sons |
| Total Pages | : 226 |
| Release | : 2011-10-24 |
| Genre | : Mathematics |
| ISBN | : 1118030990 |
A complete introduction to the many mathematical tools used to solve practical problems in coding. Mathematicians have been fascinated with the theory of error-correcting codes since the publication of Shannon's classic papers fifty years ago. With the proliferation of communications systems, computers, and digital audio devices that employ error-correcting codes, the theory has taken on practical importance in the solution of coding problems. This solution process requires the use of a wide variety of mathematical tools and an understanding of how to find mathematical techniques to solve applied problems. Introduction to the Theory of Error-Correcting Codes, Third Edition demonstrates this process and prepares students to cope with coding problems. Like its predecessor, which was awarded a three-star rating by the Mathematical Association of America, this updated and expanded edition gives readers a firm grasp of the timeless fundamentals of coding as well as the latest theoretical advances. This new edition features: * A greater emphasis on nonlinear binary codes * An exciting new discussion on the relationship between codes and combinatorial games * Updated and expanded sections on the Vashamov-Gilbert bound, van Lint-Wilson bound, BCH codes, and Reed-Muller codes * Expanded and updated problem sets. Introduction to the Theory of Error-Correcting Codes, Third Edition is the ideal textbook for senior-undergraduate and first-year graduate courses on error-correcting codes in mathematics, computer science, and electrical engineering.
| Author | : Florence Jessie MacWilliams |
| Publisher | : |
| Total Pages | : 762 |
| Release | : 1978 |
| Genre | : Error-correcting codes (Information theory) |
| ISBN | : |
