Error-correcting linear codes : classification by isometry and applications / Anton Betten
Material type: TextPublisher number: :International Book Distributors | :Flat No 17, Prakash Apartment 4405/2, 5 Ansari Road Darya Ganj New Delhi Series: Algorithms and computation in mathematics, v. 18Publication details: Berlin ; New York : Springer, ©2006Description: xxix, 798 pages 24cmISBN: 9783642421815Subject(s): Mathematics | General principles of mathematics | Combinatorial analysis | Error-correcting codes (Information theory) | Coding theory | Analyse combinatoire | Codes correcteurs d'erreurs (Théorie de l'information)DDC classification: 511.6 BETItem type | Current library | Call number | Status | Notes | Date due | Barcode | Item holds |
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Mathematics Departmental Library | SNU LIBRARY | 511.6 BET (Browse shelf(Opens below)) | Not For Loan | FPDA Grant | M316 |
This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes. Up until now, these advanced topics have only been covered in research papers. The present book provides access to these results at a level which is suitable for graduate students of mathematics, computer science and engineering as well as for researchers
This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes. Up until now, these advanced topics have only been covered in research papers. The present book provides access to these results at a level which is suitable for graduate students of mathematics, computer science and engineering as well as for researchers
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