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.

Contents

• Introduction
  • Block Error-correcting Codes
  • Basic concepts
  • Linear codes
  • Hadamard codes
  • Parameter bounds

• Finite Fields
  • Z_n and F_p
  • Construction of finite fields
  • Structure of the multiplicative group of a finite field
  • Minimum polynomial

• Cyclic Codes
  • Generalities
  • Effective factorization of Xⁿ - 1
  • Roots of a cyclic code
  • The Meggitt decoder

• Alternant Codes
  • Definitions and examples
  • Error location, error evaluation and the key equation
  • The Berlekamp-Massey-Sugiyama algorithm
  • The Peterson-Gorenstein-Zierler algorithm

• Appendix: The WIRIS/cc system
• Index of Symbols
• Index of Symbols
• Alphabetic Index, Glossary and Notes