Error-correcting Linear Codes Classification by Isometry And Applications

The subject of the book is error-correcting linear codes. It contains an introduction to the theory of these codes, their classification according to isometry (which gathers codes of the same error correcting quality into classes), the enumeration of these classes, the construction and random generation of representatives of the isometry classes, and their applications for example to audio compact discs. Further, the authors give algorithms for the computation of the minimum distance of linear codes and for the construction of linear codes with prescribed minimum distance.An attached compact disc contains additional material in the form of data of isometry classes of optimal codes over small finite fields and executable programs (MS Windows, Linux) for studying and analyzing further properties of codes. The required methods from computeralgebra and computational group theory are carefully described.Betten, Anton is the author of 'Error-correcting Linear Codes Classification by Isometry And Applications', published 2006 under ISBN 9783540283713 and ISBN 3540283714.