Designs, Graphs, Codes and their Links [Hardcover]

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.Aimed at advanced undergraduate students or beginning graduates, this book stresses the connection between, and the applications of, design theory to graphs and codes as well as relevant topics for discussion from the theory of graphs and codes.Aimed at advanced undergraduate students or beginning graduates, this book stresses the connection between, and the applications of, design theory to graphs and codes as well as relevant topics for discussion from the theory of graphs and codes.This book stresses the connection between, and the applications of, design theory to graphs and codes. Beginning with a brief introduction to design theory and the necessary background, the book also provides relevant topics for discussion from the theory of graphs and codes.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.