Error-Correcting Linear Codes: Classification by Isometry and Applications: 18 (Algorithms and Computation in Mathematics, 18) - Hardcover

Betten, Anton; Braun, Michael; Fripertinger, Harald; Kerber, Adalbert; Kohnert, Axel; Wassermann, Alfred

Hardcover

ISBN 10: 3540283714 ISBN 13: 9783540283713

Publisher: Springer, 2006

Synopsis

This text offers an introduction to error-correcting linear codes for graduate students in mathematics, computer science and engineering and researchers. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic concepts like finite fields and group actions are developed rigorously. Cyclic codes are discussed in great detail, as well as their application in CD players.In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically with or without a prescribed automorphism group. Furthermore, lattice basis reduction is presented as a tool for computing generator matrices and the minimum distance of codes. The attached CD provides access to generator matrices of more than 70000 nonisometric optimal codes, covering all optimal codes for a given set of code parameters. It also contains software for evaluating minimum distances, weight enumerators, and for the construction of codes.

About this title

Product Description:

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.

Review:

From the reviews:

"The theory of error-correcting codes is a ... new addition to the list of mathematical disciplines. ... This book contains 51 figures and 102 tables. ... The book provides access to all results at a level which is proper for graduate students of mathematics and computer science as well as for researchers." (Zlatko Varbanov, Zentralblatt MATH, Vol. 1102 (4), 2007)

"This is a thorough treatment of the theory of error-correcting codes. ... This book is remarkable because of the enormous amount of material presented (in a very lucid style), but also because of the great variety of mathematical disciplines used ... . A beautiful book on applied mathematics!" (H. Mitsch, Monatshefte für Mathematik, Vol. 151 (3), 2007)

"The main object of the book under review is an error-correcting linear code. ... a motivated reader can profit much from studying this monograph, which contains rich material in one of the rapidly developing areas. ... The presentation of material is reader-friendly, arguments are clear and concise, numerous exercises are original and stimulating ... . To sum up, the book under review can be strongly recommended to anyone interested in the topic." (Boris È. Kunyavskii, Mathematical Reviews, Issue 2008 h)

About this edition

• Publisher: Springer
• Publication date: 2006
• ISBN 10: 3540283714
• ISBN 13: 9783540283713
• Binding: Hardcover
• Number of pages: 827