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Cameron P.J., Van Lint J.H. Designs, Graphs, Codes and their Links

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Cameron P.J., Van Lint J.H. Designs, Graphs, Codes and their Links
Издательство Cambridge University Press, 1991, -251 pp.
The three subjects of this book all began life in the provinces of applicable mathematics. Design theory originated in statistics (its name reflects its initial use, in experimental design); codes in information transmission; and graphs in the modelling of networks of a very general kind (in the first instance, the bridges of Konigsberg). All three have since become part of mainstream discrete mathematics.
We have not tried to write a textbook on three individual topics. Instead, our goal is more limited: we want to explore some of the ways in which the three topics have interacted with each other, with results and methods from one area being applied in another. Indeed, we believe that discrete mathematics is better defined by its methods than by its subject-matter, and our approach reflects this.
The book has its origins in the notes of two series of lectures given by the authors at Westfield College, London, at the invitation of Dan Hughes. The audience at those lectures consisted of design theorists, and our job was to show them that graphs and codes could be useful to them. The notes subsequently appeared in the London Mathematical Society Lecture Note Series in 1975, and in a considerably revised form in 1980. We tried then to make the notes accessible to a wider audience by adding an introductory chapter on design theory.
In the intervening decade, we have become aware that a number of students used the book as a textbook. Their task was not made easier by the 'research notes' style in which many assertions are left without proof. Accordingly, when David Tranah approached us about a new revision, we decided to re-write the book completely, turning it into a textbook. We have expanded considerably the chapters on design theory, strongly regular graphs, and codes; we have, wherever possible, included proofs of our assertions, and avoided words like 'clearly .'; and we have added a number of exercises, with hints where appropriate.
In addition, we have brought the material up-to-date, with a number of new topics (including graphs with least eigenvalue —2 and their connection with root systems, strongly regular graphs with strongly regular subconstituents, and expanded treatments of two-graphs, partial geometries, Preparata and Kerdock codes, two-weight projective codes, P- and Q-polynomial association schemes, etc.), as well as smaller additions.
Design theory.
Strongly regular graphs.
Graphs with least eigenvalue —2.
Regular two-graphs.
Quasi-symmetric designs.
A property of the number six.
Partial geometries.
Graphs with no triangles.
Cyclic codes.
The Golay codes.
Reed-Muller and Kerdock codes.
Self-orthogonal codes and projective planes.
Quadratic residue codes and the Assmus-Mattson Theorem.
Symmetry codes over F3.
Nearly perfect binary codes and uniformly packed codes.
Association schemes.
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