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.

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"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." (J�rgen M�ller, Mathematical Reviews, Issue 2007 d)

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