The theory of error-correction codes

✍ Scribed by Florence Jessie MacWilliams; N J A Sloane

• Publisher: North-Holland
• Year: 1977
• Tongue: English
• Leaves: 785
• Series: NHML0016
• Category: Library

✦ Table of Contents

Front Cover......Page 1
Preface......Page 7
Preface to the third printing......Page 13
Contents......Page 15
1. Linear codes......Page 24
2. Nonlinear codes, Hadamardmatrices, designs andthe Golay code......Page 61
3. An introduction to BCH codes and finite fields......Page 103
4. Finite fields......Page 116
5. Dual codes and their weight distribution......Page 148
6. Codes, designs and perfectcodes......Page 178
7. Cyclic codes......Page 211
8. Cyclic codes (cont.): Idempotents and Mattson Solomon polynomials......Page 239
9. BCH codes......Page 280
10. Reed-Solomon and Justesen codes......Page 317
11. MDS codes......Page 340
12. Alternant, Goppa and other generalized BCH codes......Page 355
13. Reed-Muller codes......Page 393
14. First-order Reed-Muller codes......Page 429
15. Second-order Reed-Muller, Kerdock and Preparata codes......Page 456
16. Quadratic-residue codes......Page 503
17. Bounds on the size of a code......Page 546
18. Methods for combining codes......Page 590
19. Self-dual codes and invariant theory......Page 619
20. The Golay codes......Page 657
21. Association schemes......Page 674
Appendix A - Tables of the bestcodes known......Page 696
Appendix B - Finite geometries......Page 715
Bibliography......Page 726
Index......Page 780