Designs, Graphs, Codes and their Links

Designs, Graphs, Codes and their Links

by P. J. Cameron, J. H. van Lint
     
 

Although design theory, graph theory and coding theory, had their origins in various areas of applied mathematics, today they are found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on designs, graphs and codes, into an invaluable textbook. They do not seek to consider each of these… See more details below

Overview

Although design theory, graph theory and coding theory, had their origins in various areas of applied mathematics, today they are found under the umbrella of discrete mathematics. Here the authors have considerably reworked and expanded their earlier successful books on designs, graphs and codes, 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 throughout, and a large number of references are given.

Product Details

ISBN-13:
9780521413251
Publisher:
Cambridge University Press
Publication date:
12/28/2003
Series:
London Mathematical Society Student Texts Series, #22
Pages:
252
Product dimensions:
5.98(w) x 8.98(h) x 0.67(d)

Table of Contents

Contentsv
Prefacevii
Notation and terminologyix
1.Design theory1
2.Strongly regular graphs29
3.Graphs with least eigenvalue-249
4.Regular two-graphs57
5.Quasi-symmetric designs69
6.A property of the number six81
7.Partial geometries91
8.Graphs with no triangles105
9.Codes117
10.Cyclic codes125
11.The Golay codes131
12.Reed-Muller and Kerdock codes139
13.Self-orthogonal codes and projective planes153
14.Quadratic residue codes and the Assmus-Mattson Theorem161
15.Symmetry codes over F[subscript 3]175
16.Nearly perfect binary codes and uniformly packed codes181
17.Association schemes197
References215
Index227
List of Authors237

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