書誌事項

Graph theory, coding theory, and block designs

P.J. Cameron & J.H. Van Lint

(London Mathematical Society lecture note series, 19)

Cambridge University Press, c1975

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注記

Includes bibliographical references (p. 107-112) and index

内容説明・目次

内容説明

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.

目次

  • Introduction
  • 1. A brief introduction to design theory
  • 2. Strongly regular graphs
  • 3, Quasi-symmetric designs
  • 4. Strongly regular graphs with no triangles
  • 5. Polarities of designs
  • 6. Extension of graphs
  • 7. Codes
  • 8. Cyclic codes
  • 9. Threshold decoding
  • 10. Reed-Muller codes
  • 11. Self-orthogonal codes and designs
  • 12. Quadratic residue codes
  • 13. Symmetry codes over GF(3)
  • 14. Nearly perfect binary codes and uniformly packed codes
  • 15. Association schemes
  • References
  • Index.

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