Designs graphs codes and their links cameron p j lint j h van
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Assume that a and b are both square. Strongly regular graphs -- Exercises -- 3. Nearly perfect binary codes and uniformly packed codes; 17. Many exercises and useful hints are included througout, and a large number of references are given. We will need to use the cyclotomic numbers of order 2. Peter Jephson , 1947- Graphs, codes, and designs. Association schemes -- Exercises -- References -- Index -- List of Authors.

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. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Contents: Cover -- Title -- Copyright -- Contents -- Preface -- Notation and terminology -- 1. Strongly regular graphs with no triangles; 6. Self-orthogonal codes, designs and projective planes; 14.

Symmetry codes over F3 -- Exercises -- 16. Many exercises and useful hints are included througout, and a large number of references are given. The E-mail message field is required. Self-orthogonal codes and projective planes -- Exercises -- 14. Partial geometries -- Exercises -- 8. The Golay codes -- Exercises.

Cyclic codes -- Exercises -- 11. The three subjects of this book all began life in the provinces of applicable mathematics. A property of the number six -- Exercises -- 7. Codes -- Exercises -- 10. The discrete mathematics needed is developed in the text, making this book accessible to any student with a background of undergraduate algebra.

Acknowledgements The authors are very grateful to the three anonymous referees and to the Coordinating Editor for all of their detailed comments that greatly improved the quality and the presentation of this paper. 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. We construct several classes of these, and discuss some of the restrictions on the parameters of such a class. 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. They do not seek to consider each of these three topics individually, but rather to stress the many and varied connections between them. Quasi-symmetric designs -- Exercises -- 6. In this paper we discuss a particular class of 3-adesigns, i.

Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, into an invaluable textbook. Design theory originated in statistics its name reflects its initial use, in experimental design ; codes in information transmission; and graphs in the modeling of networks of a very general kind in the first instance, the bridges of Konigsberg. They do not seek to consider each of these three topics individually, but rather to stress the many and varied connections between them. All three have since become a part of mainstream discrete mathematics. Appendix We will need some facts about cyclotomic classes and cyclotomic numbers.

Nearly perfect binary codes and uniformly packed codes -- The Preparata codes. Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, into an invaluable textbook. The E-mail message field is required. Reed-Muller and Kerdock codes -- Constructions of Kerdock sets. Finite geometries and codes; 13. .

Graphs with no triangles -- Exercises -- 9. Graphs with least eigenvalue -2 -- Exercises -- 4. A brief introduction to design theory; 2. We also construct several new classes of 2-adesigns, and discuss some of their properties as well. Regular two-graphs -- Exercises -- 5.

Quadratic residue codes and the Assmus-Mattson Theorem -- Exercises -- 15. 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. 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. The discrete mathematics needed is developed in the text, making this book accessible to any student with a background of undergraduate algebra.