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.

InhaltsangabeThe Type of a Self-Dual Code.- Weight Enumerators and Important Types.- Closed Codes.- The Category Quad.- The Main Theorems.- Real and Complex Clifford Groups.- Classical Self-Dual Codes.- Further Examples of Self-Dual Codes.- Lattices.- Maximal Isotropic Codes and Lattices.- Extremal and Optimal Codes.- Enumeration of Self-Dual Codes.- Quantum Codes.