Graph Theory, Coding Theory and Block Designs

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

doi:10.1017/CBO9781107325425

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.

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Contents

Frontmatter
pp i-ii
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Contents
pp iii-iv
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Introduction
pp v-vi
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1 - A brief introduction to design theory
pp 1-10
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2 - Strongly regular graphs
pp 11-18
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3 - Quasi-symmetric designs
pp 19-24
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4 - Strongly regular graphs with no triangles
pp 25-32
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5 - Polarities of designs
pp 33-37
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6 - Extension of graphs
pp 38-43
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7 - Codes
pp 44-50
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8 - Cyclic codes
pp 51-56
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9 - Threshold decoding
pp 57-58
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10 - Reed-Muller codes
pp 59-64
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11 - Self-orthogonal codes and designs
pp 65-70
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12 - Quadratic residue codes
pp 71-80
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13 - Symmetry codes over GF(3)
pp 81-86
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14 - Nearly perfect binary codes and uniformly packed codes
pp 87-95
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15 - Association schemes
pp 96-106
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References
pp 107-112
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Index
pp 113-114
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Graph Theory, Coding Theory and Block Designs

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Contents

Frontmatter
pp i-ii

Contents
pp iii-iv

Introduction
pp v-vi

1 - A brief introduction to design theory
pp 1-10

2 - Strongly regular graphs
pp 11-18

3 - Quasi-symmetric designs
pp 19-24

4 - Strongly regular graphs with no triangles
pp 25-32

5 - Polarities of designs
pp 33-37

6 - Extension of graphs
pp 38-43

7 - Codes
pp 44-50

8 - Cyclic codes
pp 51-56

9 - Threshold decoding
pp 57-58

10 - Reed-Muller codes
pp 59-64

11 - Self-orthogonal codes and designs
pp 65-70

12 - Quadratic residue codes
pp 71-80

13 - Symmetry codes over GF(3)
pp 81-86

14 - Nearly perfect binary codes and uniformly packed codes
pp 87-95

15 - Association schemes
pp 96-106

References
pp 107-112

Index
pp 113-114

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Graph Theory, Coding Theory and Block Designs

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