Designs, Graphs, Codes and their Links ( London Mathematical Society Student Texts )

Publication series :London Mathematical Society Student Texts

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

Publisher: Cambridge University Press‎

Publication year: 1991

E-ISBN: 9780511879951

P-ISBN(Paperback): 9780521413251

Subject: O157 Combinatorial Mathematics (combinatorics)

Keyword: 图解数学、图算数学

Language: ENG

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Designs, Graphs, Codes and their Links

Description

Although graph theory, design theory, and coding theory had their origins in various areas of applied mathematics, today they are to be found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on graphs, codes and designs, into an invaluable textbook. They do not seek to consider each of these three topics individually, but rather to stress the many and varied connections between them. The discrete mathematics needed is developed in the text, making this book accessible to any student with a background of undergraduate algebra. Many exercises and useful hints are included througout, and a large number of references are given.

Chapter

Appendix: The Principle of Inclusion and Exclusion

Exercises

2. Strongly regular graphs

Exercises

3. Graphs with least eigenvalue —2

Exercises

4. Regular two-graphs

Exercises

5. Quasi-symmetric designs

Exercises

6. A property of the number six

Exercises

7. Partial geometries

Exercises

8. Graphs with no triangles

Exercises

9. Codes

Exercises

10. Cyclic codes

Exercises

11. The Golay codes

Exercises

12. Reed-Muller and Kerdock codes

Constructions of Kerdock sets.

Exercises

13. Self-orthogonal codes and projective planes

Exercises

14. Quadratic residue codes and the Assmus-Mattson Theorem

Exercises

15. Symmetry codes over F3

Exercises

16. Nearly perfect binary codes and uniformly packed codes

The Preparata codes.

Exercises.

17. Association schemes

Exercises

References

Index

List of Authors

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