Graphs, Codes and Designs

P. J. Cameron; J. H. van Lint

doi:10.1017/CBO9780511662140

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.

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Graphs, Codes and Designs

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

1 - A brief introduction to design theory
pp 1-15

2 - Strongly regular graphs
pp 16-24

3 - Quasi-symmetric designs
pp 25-31

4 - Partial geometries
pp 32-36

5 - Strongly regular graphs with no triangles
pp 37-44

6 - Polarities of designs
pp 45-48

7 - Extensions of graphs
pp 49-55

8 - 1-factorisations of K6
pp 56-60

9 - Codes
pp 61-67

10 - Cyclic codes
pp 68-73

11 - Threshold decoding
pp 74-75

12 - Finite geometries and codes
pp 76-83

13 - Self-orthogonal codes, designs and projective planes
pp 84-94

14 - Quadratic residue codes
pp 95-106

15 - Symmetry codes over GF(3)
pp 107-112

16 - Nearly perfect binary codes and uniformly packed codes
pp 113-123

17 - Association schemes
pp 124-135

References
pp 136-144

Index
pp 145-147

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Graphs, Codes and Designs

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