Error-correcting linear codes : classification by isometry and applications
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 a...
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edizione: | 1st ed. 2006. |
| Serie: | Algorithms and computation in mathematics
18 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 24 mars 2011 Autres contributeurs : Adalbert Kerber, Axel Kohnert, Alfred Wassermann (auteurs) Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Error-correcting linear codes, classification by isometry and applications, Anton Betten, Michael Braun, Harald Fripertinger [et al.], 2006, Berlin, Springer, 1 vol. (XXIX-798 p.), Algorithms and computation in mathematics, 3-540-28371-4 |
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| 100 | 1 | |a Betten, Anton. | |
| 245 | 1 | 0 | |a Error-correcting linear codes : |b classification by isometry and applications |c by Anton Betten, Michael Braun, Harald Fripertinger ... [et al.]. |
| 250 | |a 1st ed. 2006. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Algorithms and computation in mathematics |v 18 | |
| 500 | |a Description d'après consultation du 24 mars 2011 | ||
| 500 | |a Autres contributeurs : Adalbert Kerber, Axel Kohnert, Alfred Wassermann (auteurs) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. p. [771]-783. Index | ||
| 505 | 1 | |a 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. | |
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Codes correcteurs d'erreurs (théorie de l'information) | ||
| 650 | |a Corps finis | ||
| 650 | |a Actions de groupes (mathématiques) | ||
| 700 | 1 | |a Kerber, Adalbert, |d 1939- |4 aut | |
| 700 | 1 | |a Braun, Michael, |d 19..- |4 aut | |
| 700 | 1 | |a Fripertinger, Harald, |d 1965- |4 aut | |
| 700 | 1 | |a Kohnert, Axel, |d 19..- |4 aut | |
| 700 | 1 | |a Wassermann, Alfred, |d 1963- |4 aut | |
| 776 | 0 | |0 111521009 |t Error-correcting linear codes |o classification by isometry and applications |f Anton Betten, Michael Braun, Harald Fripertinger [et al.] |d 2006 |c Berlin |n Springer |p 1 vol. (XXIX-798 p.) |s Algorithms and computation in mathematics |z 3-540-28371-4 | |
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