Designs and Their Codes

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Cambridge University Press, Jan 6, 1994 - Mathematics - 364 pages
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Algebraic coding theory has in recent years been increasingly applied to the study of combinatorial designs. This book gives an account of many of those applications together with a thorough general introduction to both design theory and coding theory developing the relationship between the two areas. The first half of the book contains background material in design theory, including symmetric designs and designs from affine and projective geometry, and in coding theory, coverage of most of the important classes of linear codes. In particular, the authors provide a new treatment of the Reed-Muller and generalized Reed-Muller codes. The last three chapters treat the applications of coding theory to some important classes of designs, namely finite planes, Hadamard designs and Steiner systems, in particular the Witt systems.
 

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Contents

Designs
1
Codes
25
The geometry of vector spaces
89
Symmetric Designs
117
The standard geometric codes
139
Codes from planes
199
Hadamard designs
249
Steiner systems
295
Bibliography
317
Glossary
337
Index of Terms
344
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