This book is concerned with the relations between graphs, error-correcting codes and designs, in particular how techniques of graph theory and coding theory can give information about designs. A major revision and expansion of a previous volume in this series, this account includes many examples and new results as well as improved treatments of older material. So that non-specialists will find the treatment accessible the authors have included short introductions to the three main topics. This book will be welcomed by graduate students and research mathematicians and be valuable for advanced courses in finite combinatorics.
Author(s): P. J. Cameron, J. H. van Lint
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1980
Language: English
Pages: 155
Contents......Page 5
Preface......Page 7
1. A brief introduction to design theory......Page 9
2. Strongly regular graphs......Page 24
3. Quasi-symmetric designs......Page 33
4. Partial geometries......Page 40
5. Strongly regular graphs with no triangles......Page 45
6. Polarities of designs......Page 53
7. Extensions of graphs......Page 57
8. 1-factorisations of K_6......Page 64
9. Codes......Page 69
10. Cyclic codes......Page 76
11. Threshold decoding......Page 82
12. Finite geometries and codes......Page 84
13. Self-orthogonal codes, designs and projective planes......Page 92
14. Quadratic residue codes......Page 103
15. Symmetry codes over GF(3)......Page 115
16. Nearly perfect binary codes and uniformly packed codes......Page 121
17. Association schemes......Page 132
References......Page 144
Index......Page 153
