Synopses & Reviews
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.
"...a valuable resource for researchers in either finite geometries or coding theory as well as for algebraists who want to learn about this lively, growing area." Vera Pless, Mathematical Reviews"...the relationship between the two subjects is very much a two-way channel, and the book is a mine of useful information from whichever direction one approaches it....a useful compilation of material which, together with the extensive bibliography, will prove useful to anyone whose research impinges on these topics." N.L. Biggs"...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
A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.
This is a self-contained and up-to-date account of the applications of algebraic coding theory to the study of combinatorial designs. Whilst the book is aimed at mathematicians working in either coding theory or combinatorics, it is designed to be used by non-specialists and so is of value to graduate students or computer scientists working in those areas.
Algebraic coding has in recent years been increasingly applied to the study of combinatorial designs. Designs and their Codes gives an account of many of these applications together with a thorough general introduction to both design theory and code theory ñdeveloping the relationship between the two areas.
An up-to-date, self-contained account of algebraic coding theory as it is applied to the study of combinatorial designs.
Table of Contents
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.