Graphs, Codes and Designs

Graphs, Codes and Designs

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Cambridge University Press

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Graphs, Codes and Designs

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.

Product Details

ISBN-13: 9780521231411
Publisher: Cambridge University Press
Publication date: 01/28/2008
Series: London Mathematical Society Lecture Note Series , #43
Pages: 156
Product dimensions: 5.90(w) x 8.90(h) x 0.50(d)

Table of Contents

1. A brief introduction to design theory; 2. Strongly regular graphs; 3. Quasi-symmetric designs; 4. Partial geometries; 5. Strongly regular graphs with no triangles; 6. Polarities of designs; 7. Extensions of graphs; 8. 1-factorisations of K6; 9. Codes; 10. Cyclic codes; 11. Threshold decoding; 12. Finite geometries and codes; 13. Self-orthogonal codes, designs and projective planes; 14. Quadratic residue codes; 15. Symmetry codes over GF(3); 16. Nearly perfect binary codes and uniformly packed codes; 17. Association schemes.

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