A Course in Algebraic Error-Correcting Codes


Book Description

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 Error-correcting Codes


Book Description

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.




The BioMechanics Method for Corrective Exercise


Book Description

The BioMechanics Method for Corrective Exercise enables health and fitness professionals to identify common musculoskeletal imbalances in their clients and apply appropriate corrective exercises to swiftly eliminate muscle and joint pain and improve physical function.




A First Course in Proof Correcting


Book Description

Textbook on proofreading techniques in publishing - aimed at authors, printing workers and the professional proofreader, covers elements of style, copyright, page make-up, setting of tables, printing in foreign languages, etc., And includes numerous exercises. Diagrams and illustrations.




An Introduction to Error Correcting Codes with Applications


Book Description

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.




Introduction to the Theory of Error-Correcting Codes


Book Description

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.




Correcting Corrections


Book Description

Correcting Corrections is a plan to control the horrendous crime and prison problem along with the associated social issues in the United States of America.




A Practitioner’s Guide to Correcting Mistakes in Pension Schemes


Book Description

The discovery of mistakes in pension scheme documents is as common as it is potentially serious for the administration of the scheme and for the sponsoring employer. The large sums invested in pension schemes mean that such mistakes are often very costly indeed. This book provides a practical guide to the different methods available to correct commonly-occurring mistakes in the governing provisions of pension schemes. It combines a detailed review of the law with (where relevant) practical tips, including analysis of the appropriate practice and procedure involved in the key methods of correction. With a significant body of case law enabling more authoritative answers to be given to the legal issues affecting the correction of pension scheme mistakes, and more and more mistakes being discovered because of the move to secure pension scheme liabilities with insurance companies, trustees and employers need swift and accurate legal advice on what they can do to correct such mistakes. This book provides them and their legal advisers with that advice ensuring they do not make the same costly mistakes that others have made. This book will help the reader to: · To select the most appropriate method of correcting the mistake · Consider including provisions in the terms of the pension scheme which may make the correction of the mistake easier and cheaper · Select the most tax-efficient way of correcting the mistake · Understand the processes involved in correcting the mistake · Better advise their clients as to how to deal with the mistake This title is included in Bloomsbury Professional's Pensions Law online service.




Transactions


Book Description




The World's Work


Book Description

A history of our time.