Overview
- A monumental work - the definitive account on the topic
Part of the book series: Algorithms and Computation in Mathematics (AACIM, volume 17)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
Keywords
About this book
One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory. 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 self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.
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 that are presently known. Besides self-dual codes, the book also discusses two closely-related subjects, lattices and modular forms, and quantum error-correcting codes.
This book, written by the leading experts in the subject, has no equivalent in the literature and will be of great interest to mathematicians, communication theorists, computer scientists and physicists.
Reviews
From the reviews:
"This book under review the general notions of form rings and their representations … . This book, introducing a new unifying theory and its applications to a wealth of substantial examples, is certainly written for experts in the field." (Jürgen Müller, Mathematical Reviews, Issue 2007 d)
Authors and Affiliations
Bibliographic Information
Book Title: Self-Dual Codes and Invariant Theory
Authors: Gabriele Nebe, Eric M. Rains, Neil J.A. Sloane
Series Title: Algorithms and Computation in Mathematics
DOI: https://doi.org/10.1007/3-540-30731-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-30729-7Published: 09 February 2006
Softcover ISBN: 978-3-642-06801-0Published: 22 November 2010
eBook ISBN: 978-3-540-30731-0Published: 20 May 2006
Series ISSN: 1431-1550
Edition Number: 1
Number of Pages: XXVII, 430
Topics: Algebra, Coding and Information Theory, Group Theory and Generalizations, Control, Robotics, Mechatronics, Number Theory, Quantum Physics