A First Course in Coding Theory

✍ Scribed by R. A. Hill

• Publisher: Oxford University Press
• Year: 1990
• Tongue: English
• Leaves: 263
• Series: Oxford Applied Mathematics and Computing Science 1
• Category: Library

✦ Synopsis

The aim of this book is to provide an elementary treatment of the theory of error-correcting codes, assuming no more than high school mathematics and the ability to carry out matrix arithmetic. The book is intended to serve as a self-contained course for second or third year mathematics undergraduates, or as a readable introduction to the mathematical aspects of coding for students in engineering or computer science.

✦ Table of Contents

Hill, R. A first course in coding theory(Oxford Applied Mathematics and Computing Science )(OUP,1 ed.1990) ......Page 4
Preface Vii ......Page 7
Acknowledgements viii ......Page 8
Contents ix ......Page 9
Notation xi ......Page 10
1 Introduction to error-correcting codes 1 ......Page 12
2 The main coding theory problem 11 ......Page 22
3 An introduction to finite fields 31 ......Page 42
4 Vector spaces over finite fields 41 ......Page 52
5 Introduction to linear codes 47 ......Page 58
6 Encoding and decoding with a linear code 55 ......Page 66
7 The dual code, the parity-check matrix, and syndrome decoding 67 ......Page 78
8 The Hamming codes 81 ......Page 92
9 Perfect codes 97 ......Page 108
10 Codes and Latin squares 113 ......Page 124
11 A double-error correcting decimal code and an introduction to BCH codes 125 ......Page 136
12 Cyclic codes 141 ......Page 152
13 Weight enumerators 165 ......Page 176
14 The main linear coding theory problem 175 ......Page 186
15 MDS codes 191 ......Page 202
16 Concluding remarks, related topics, and further reading 201 ......Page 212
Solutions to exercises 211 ......Page 222
Bibliography 243 ......Page 254
Index 249 ......Page 260
cover ......Page 1

✦ Subjects

Информатика и вычислительная техника;Теория информации и корректирующие коды;