Error-Correcting Linear Codes: Classification by Isometry and Applications / Edition 1

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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, as well as their application in CD players. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically. The attached CD includes access to generator matrices of more than 70,000 nonisometric optimal codes.

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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9783540283713
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 10/5/2006
  • Series: Algorithms and Computation in Mathematics Series, #18
  • Edition description: 2006
  • Edition number: 1
  • Pages: 798
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.75 (d)

Table of Contents

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.

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