Graph Theory, Coding Theory and Block Designs [Paperback]

These are notes deriving from lecture courses on the theory of t-designs and graph theory given by the authors in 1973 at Westfield College, London.These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs and graph theory. Topics from a wide range of finite combinatorics are covered and the book will interest all scholars of combinatorial theory.These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs and graph theory. Topics from a wide range of finite combinatorics are covered and the book will interest all scholars of combinatorial theory.These are notes deriving from lecture courses given by the authors in 1973 at Westfield College, London. The lectures described the connection between the theory of t-designs on the one hand, and graph theory on the other. A feature of this book is the discussion of then-recent construction of t-designs from codes. Topics from a wide range of finite combinatorics are covered and the book will interest all scholars of combinatorial theory.Introduction; 1. A brief introduction to design theory; 2. Strongly regular graphs; 3, Quasi-symmetric designs; 4. Strongly regular graphs with no triangles; 5. Polarities of designs; 6. Extension of graphs; 7. Codes; 8. Cyclic codes; 9. Threshold decoding; 10. ReedMuller codes; 11. Self-orthogonal codes and designs; 12. Quadratic residue codes; 13. Symmetry codes over GF(3); 14. Nearly perfect binary codes and uniformly packed codes; 15. Association schemes; References; Index.