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 which has inspired hundreds
of papers 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 extensive encyclopedia listing the different types
of self-dual codes and their properties, including tables of the best
codes presently known. Beyond 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.