# Error correcting Codes

## Error correcting Codes

The coding problem; Introduction to algebra; Linear codes; Error correction capabilities of linear codes; Important linear block codes; Polynomial rings and galois fields; Linear switching circuits; Cyclic codes; Bose-chaudhuri-hocquenghem codes; Arithmetic codes.

# Fundamentals of Error Correcting Codes

## Fundamentals of Error Correcting Codes

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.

# Introduction to Coding Theory

## Introduction to Coding Theory

This 2006 book introduces the theoretical foundations of error-correcting codes for senior-undergraduate to graduate students.

# Introduction to the Theory of Error correcting Codes

## Introduction to the Theory of Error correcting Codes

An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book. It considers such codes as Hamming codes and Golay codes, correction of double errors, use of finite fields, cyclic codes, BCH codes and weight distributions, as well as design of codes. In this second edition, the author includes more material on non-binary code and cyclic codes. In addition some proofs have been simplified and there are many more examples and problems. The text has been aimed at mathematicians, electrical engineers and computer scientists.

# Error Correcting Linear Codes

## Error Correcting Linear Codes

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 First Course in Coding Theory

## A First Course in Coding Theory

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.

# Coding Theory

## Coding Theory

Modern introduction to theory of coding and decoding with many exercises and examples.

# A Practical Guide to Error Control Coding Using MATLAB

## A Practical Guide to Error Control Coding Using MATLAB

This practical resource provides you with a comprehensive understanding of error control coding, an essential and widely applied area in modern digital communications. The goal of error control coding is to encode information in such a way that even if the channel (or storage medium) introduces errors, the receiver can correct the errors and recover the original transmitted information. This book includes the most useful modern and classic codes, including block, Reed Solomon, convolutional, turbo, and LDPC codes.You find clear guidance on code construction, decoding algorithms, and error correcting performances. Moreover, this unique book introduces computer simulations integrally to help you master key concepts. Including a companion DVD with MATLAB programs and supported with over 540 equations, this hands-on reference provides you with an in-depth treatment of a wide range of practical implementation issues.

# Introduction to Error Control Codes

## Introduction to Error Control Codes

This textbook provides a firm foundation to the field of error control codes, leading the student step by step through this complex topic, beginning with single parity code checks and repetition codes. Through these basic error-control mechanisms the fundamental principles of error detectionand correction, minimum distance and error-control limits are considered. The reader is guided from basic error-control codes through to linear codes, cyclic codes, linear feedback shift registers, vector fields, Galois fields, BCH codes and convolutional codes. Complex mathematical proofs areomitted where possible to keep the text concise and easy-to-follow.Additional notes on the contents:*Chapter 2 the treatment of linear codes in this chapter avoids reference to vector spaces, enabling the reader to gain an understanding of linear codes sufficient to move onto cyclic codes without the distraction of the complexity of vector spaces.*Chapter 5 considers vector spaces and revisits linear codes in the context of vector spaces.*Chapter 6 starts with the ordinary concepts of sets and gently leads the reader through the principles of groups and fields, the end goal being an understanding of Galois fields that will enable the reader to understand the BCH codes considered in Chapter 7.

# An Introduction to Error Correcting Codes with Applications

## An Introduction to Error Correcting Codes with Applications

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.