Designs and their Codes [Paperback]

A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.An up-to-date, self-contained account of algebraic coding theory as it is applied to the study of combinatorial designs.An up-to-date, self-contained account of algebraic coding theory as it is applied to the study of combinatorial designs.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.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. ...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 analysilól