Designs, Graphs, Codes and their Links

This book demonstrates the connection between, and the applications of, design theory to graphs and codes. It is suitable as a textbook for advanced undergraduate students.

P. J. Cameron (Author), J. H. van Lint (Author)

9780521423854, Cambridge University Press

Paperback, published 19 September 1991

252 pages, 10 b/w illus.
23.6 x 15.8 x 2 cm, 0.38 kg

Although graph theory, design theory, and coding theory had their origins in various areas of applied mathematics, today they are to be found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, 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 througout, and a large number of references are given.

1. Design theory
2. Strongly regular graphs
3. Graphs with least eigenvalue -2
4. Regular two-graphs
5. Quasi-symmetric designs
6. A property of the number 6
7. Partial geometries
8. Graphs with no triangles
9. Codes
10. Cyclic codes
11. The Golay codes
12. Reed-Muller codes
13. Self-dual codes and projective plane
14. Quadratic residue codes and the Assmus-Mattson theorem
15. Symmetry codes over F3
16. Nearly perfect binary codes and uniformly packed codes
17. Association schemes.

Subject Areas: Combinatorics & graph theory [PBV]