ENGLISH

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

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

Book information

Year
2006
ISBN
3540283714, 9783540283713
Open Library ID
OL9055843M
Language
english
Format
PDF
Filesize
4 MB (4381550 bytes)
Edition
1
Pages
828\829
Time added
2011-06-04 13:46:07

Description

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.

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