This is the web site for our book, Self-Dual Codes and Invariant Theory, which was published by Springer, Berlin, in Feb 2006.
It is Volume 17 of the series Algorithms and Computation in Mathematics; ISBN 3-540-30729-X, xxiii+430 pp.
To go to the Springer site for this book, click here.
To order from Amazon: click here.
One of the most remarkable theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes. In the past 35 years there have been hundreds of papers written about generalizations and applications of this theorem to different types of codes. This book develops a new theory which includes all the earlier generalizations at once. It is also in part an encyclopedia that gives a very extensive list of the different types of self-dual codes and their properties, including tables of the best codes as far as they are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes.
The book will be of interest to people working in the areas of
- error-correcting codes - lattices, quadratic forms and modular forms - group theory, invariant theory, number theory - quantum computers
- electrical engineers - mathematicians - computer scientists - physicists
Open Problems. In this connection we would like to mention the following open problems.