This text offers an introduction to error-correcting linear codes. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. It is based on the successful German edition. The relevant algebraic concepts like finite fields and group actions 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 with or without a prescribed automorphism group.
Rezensionen / Stimmen
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)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Graduate
Illustrationen
XXIX, 798 p. With online files/update.
Maße
Höhe: 23.5 cm
Breite: 15.5 cm
Gewicht
ISBN-13
978-3-540-28371-3 (9783540283713)
DOI
Schweitzer Klassifikation
Linear Codes.- Bounds and Modifications.- Finite Fields.- Cyclic Codes.- Mathematics and Audio Compact Discs.- Enumeration of Isometry Classes.- Solving Systems of Diophantine Linear Equations.- Linear Codes with a Prescribed Minimum Distance.- The General Case.