Block Error-Correcting Codes: A Computational Primer

✍ Scribed by Sebastià Xambó-Descamps

• Publisher: Springer
• Year: 2003
• Tongue: English
• Leaves: 226
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

Error-correcting codes have been incorporated in numerous working communication and memory systems. This book covers the mathematical aspects of the theory of block error-correcting codes together, in mutual reinforcement, with computational discussions, implementations and examples of all relevant concepts, functions and algorithms. This combined approach facilitates the reading and understanding of the subject. The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and saved by users for their own purpose.

✦ Table of Contents

Preface......Page 3
Introduction......Page 7
Block Error-correcting Codes......Page 16
Basic concepts......Page 17
Linear codes......Page 35
Hadamard codes......Page 61
Parameter bounds......Page 71
Finite Fields......Page 90
Zn and Fp......Page 92
Construction of finite fields......Page 96
Structure of the multiplicative group of a finite field......Page 109
Minimum polynomial......Page 117
Cyclic Codes......Page 123
Generalities......Page 124
Effective factorization of Xn-1......Page 133
Roots of a cyclic code......Page 140
The Meggitt decoder......Page 149
Alternant Codes......Page 152
Definitions and examples......Page 154
Error location, error evaluation and the key equation......Page 164
The Berlekamp--Massey--Sugiyama algorithm......Page 172
The Peterson--Gorenstein--Zierler algorithm......Page 180
Appendix: The WIRIS/cc system......Page 185
Index of Symbols......Page 199
Alphabetic Index, Glossary and Notes......Page 202