Designs and their Codes

A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.

E. F. Assmus (Author), J. D. Key (Author)

9780521413619, Cambridge University Press

Hardback, published 28 August 1992

364 pages, 6 b/w illus.
23.6 x 16 x 3.1 cm, 0.716 kg

"...speaks to the tremendous influence the plane of order ten has subsequently had on the analysis and classification of designs in a much broader context than projective planes...a welcome addition to a very exciting and relatively new application of an established discipline to combinatorics...a truly fascinating and useful book. It belongs on the shelves of all those who wish to be current on the state of design theory and who are seeking interesting problems in the field to pursue." M.A. Wertheimer, Bulletin of the American Mathematical Society

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. The book is aimed at mathematicians working in either coding theory or combinatorics - or related areas of algebra. The book is, however, designed to be used by non-specialists and can be used by those graduate students or computer scientists who may be working in these areas.

1. Designs
2. Codes
3. Symmetric designs
4. Geometry of vector spaces
5.The standard geometric codes
6. Codes from planes
7. Hadamard designs
8. Steiner systems
References.

Subject Areas: Mathematical theory of computation [UYA], Combinatorics & graph theory [PBV]