Algebraic coding theory is an important area of applications of representation theory. This book gives a systematic grounding in algebraic coding theory; it is used to explore connections between the theory of group algebras including the representation theory and the theory of error-correcting codes.
This book starts with an introduction to algebraic coding theory. It presumes background in the theory of group algebras and representation theory and thus provides the necessary proofs of algebraic results. Part two is devoted to group codes (ideals of group algebras). In part three the author describes the modules of the groups \(GL_ n (K)\), and \(S(n)\) and their applications in coding theory. In this part the applications in coding theory of weight-spaces (the codes 1-MLD, MDS, GGRM codes) are presented as well.
The present volume contains a cross-section of recent progress in this area. The text will be a valuable tool for both advanced graduate students and research mathematicians. The material can be used for advanced courses and seminars and will serve as a text for a graduate level course in algebraic coding theory. A number of examples are introduced. An annoted bibliography containing 96 entries increases the book’s value.