Designs, Graphs, Codes and their Links

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Overview

Although design theory, graph theory and coding theory, had their origins in various areas of applied mathematics, today they are found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on designs, graphs and codes, into an invaluable textbook. They do not seek to consider each of these three topics individually, but rather to stress the many and varied connections between them. The discrete mathematics needed is developed in the text, making this book accessible to any student with a background of undergraduate algebra. Many exercises and useful hints are included throughout, and a large number of references are given.
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Product Details

Table of Contents

Contents v
Preface vii
Notation and terminology ix
1. Design theory 1
2. Strongly regular graphs 29
3. Graphs with least eigenvalue-2 49
4. Regular two-graphs 57
5. Quasi-symmetric designs 69
6. A property of the number six 81
7. Partial geometries 91
8. Graphs with no triangles 105
9. Codes 117
10. Cyclic codes 125
11. The Golay codes 131
12. Reed-Muller and Kerdock codes 139
13. Self-orthogonal codes and projective planes 153
14. Quadratic residue codes and the Assmus-Mattson Theorem 161
15. Symmetry codes over F[subscript 3] 175
16. Nearly perfect binary codes and uniformly packed codes 181
17. Association schemes 197
References 215
Index 227
List of Authors 237
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