This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

The topic of this book is finite group actions and their use in order to approach finite unlabeled structures by defining them as orbits of finite groups of sets. Well-known examples are graph, linear codes, chemical isomers, spin configurations, isomorphism classes of combinatorial designs etc.The second edition is an extended version and puts more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.This book will be of great use to researchers and graduate students.

This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.

This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrodinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.

Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrodinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.

Die algebraische Codierungstheorie ist ein neues Teilgebiet der diskreten Mathematik, dessen Ergebnisse bei der sicheren Datenubermittlung angewandt werden. Das Buch stellt im ersten Teil ausfuhrlich die Grundlagen der algebraischen Codierungstheorie dar. Im zweiten Teil untersuchen die Autoren lineare Codes. Dabei legen sie besonderen Wert auf die Decodierung der behandelten Codes anhand eines effizienten Mehrheitsentscheidungsverfahrens.