Book contents
- Frontmatter
- Contents
- Preface
- 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
- References
- Index
Preface
Published online by Cambridge University Press: 16 March 2010
- Frontmatter
- Contents
- Preface
- 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
- References
- Index
Summary
The predecessor of this book (London Mathematical Society Lecture Note Series 19) had its origin in several short courses of lectures given by the authors at Westfield College, London, in 1973. The audience for the lectures consisted mainly of design theorists, and the aim was to present developments in graph theory and coding theory having a bearing on design theory. An introductory chapter on designs was added, for the benefit of readers without the background of the Westfield audience.
For the present volume, the format has been kept, but extensive revisions and updatings have been made. New material includes ovals in symmetric designs (Chapters 1 and 13), the inequalities of Ray-Chaudhuri and Wilson (Chapter 1), partial geometries, with the Hoffman-Chang and Hall-Connor theorems (Chapter 4), 1-factorisations of K6 (Chapter 8), equidistant codes (Chapter 12), planes and biplanes (Chapter 13), generalised quadratic residue codes and inversive planes (Chapter 14), two-weight projective codes (Chapter 16), and the Krein bound (Chapter 17).
- Type
- Chapter
- Information
- Graphs, Codes and Designs , pp. vii - viiiPublisher: Cambridge University PressPrint publication year: 1980