Block Error-Correcting Codes

by Xambo-Descamps, Sebastian

• ISBN13: 9783540003953
• ISBN10: 3540003959
• Format: Paperback
• Copyright: 2003-05-01
• Publisher: Springer Nature

Summary

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	i
Introduction	1	(12)
1 Block Error-correcting Codes	13	(88)
1.1 Basic concepts	14	(20)
1.2 Linear codes	34	(29)
1.3 Hadamard codes	63	(15)
1.4 Parameter bounds	78	(23)
2 Finite Fields	101	(40)
2.1 Zn and Fp	103	(5)
2.2 Construction of finite fields	108	(16)
2.3 Structure of the multiplicative group of a finite field	124	(9)
2.4 Minimum polynomial	133	(8)
3 Cyclic Codes	141	(38)
3.1 Generalities	142	(12)
3.2 Effective factorization of Xn -1	154	(10)
3.3 Roots of a cyclic code	164
3.4 The Meggitt decoder	113	(66)
4 Alternant Codes	179	(42)
4.1 Definitions and examples	180	(15)
4.2 Error location, error evaluation and the key equation	195	(8)
4.3 The Berlekamp-Massey-Sugiyama algorithm	203	(12)
4.4 The Peterson-Gorenstein-Zierler algorithm	215	(6)
Appendix: The WIRIS/cc system	221	(14)
Bibliography	235
Index of Symbols	231	(10)
Alphabetic Index, Glossary and Notes	241