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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. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.
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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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Error-Correcting Linear Codes
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Well-written, applications-oriented textbook on coding theory based on earlier succesful German editionWell-written, applications-oriented textbook on coding theory based on earlier succesful German editionThis text offers an introduction . Codice articolo 11800544
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Error-Correcting Linear Codes
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines. It grew out of the need to communicate information electronically, and is currently no more than 60 years old. - ing an applied discipline by de nition, a surprisingly large number of pure mathematical areas tie into Coding Theory. If one were to name just the most important connections, one would start of course with Linear Algebra, then list Algebra and Combinatorics, and further mention Number Theory and - ometry as well as Algebraic Geometry. Being a thorough introduction to the eld, this book starts from the very beginning, which is the channel model of communication in the presence of noise. From there, we develop the fundamental concepts of error-correcting codes, like the Hamming metric and the maximum likelihood decoding pr- ciple. After discussing dual codes and simple decoding procedures, this book takes an unusual turn. The standard approach would be to move on from there and introduce either more theory or present standard constructions of codes. The approach taken here is different. 832 pp. Englisch. Codice articolo 9783642421815
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Error-Correcting Linear Codes : Classification by Isometry and Applications
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Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2014
ISBN 10: 3642421814
ISBN 13: 9783642421815
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines. It grew out of the need to communicate information electronically, and is currently no more than 60 years old. - ing an applied discipline by de nition, a surprisingly large number of pure mathematical areas tie into Coding Theory. If one were to name just the most important connections, one would start of course with Linear Algebra, then list Algebra and Combinatorics, and further mention Number Theory and - ometry as well as Algebraic Geometry. Being a thorough introduction to the eld, this book starts from the very beginning, which is the channel model of communication in the presence of noise. From there, we develop the fundamental concepts of error-correcting codes, like the Hamming metric and the maximum likelihood decoding pr- ciple. After discussing dual codes and simple decoding procedures, this book takes an unusual turn. The standard approach would be to move on from there and introduce either more theory or present standard constructions of codes. The approach taken here is different. Codice articolo 9783642421815
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Error-Correcting Linear Codes
ISBN 10: 3642421814
ISBN 13: 9783642421815
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Taschenbuch. Condizione: Neu. Neuware -The fascinating theory of error-correcting codes is a rather new addition to the list of mathematical disciplines. It grew out of the need to communicate information electronically, and is currently no more than 60 years old. - ing an applied discipline by de nition, a surprisingly large number of pure mathematical areas tie into Coding Theory. If one were to name just the most important connections, one would start of course with Linear Algebra, then list Algebra and Combinatorics, and further mention Number Theory and - ometry as well as Algebraic Geometry. Being a thorough introduction to the eld, this book starts from the very beginning, which is the channel model of communication in the presence of noise. From there, we develop the fundamental concepts of error-correcting codes, like the Hamming metric and the maximum likelihood decoding pr- ciple. After discussing dual codes and simple decoding procedures, this book takes an unusual turn. The standard approach would be to move on from there and introduce either more theory or present standard constructions of codes. The approach taken here is different.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 832 pp. Englisch. Codice articolo 9783642421815
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Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics, 18)
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Error-Correcting Linear Codes : Classification by Isometry and Applications
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Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics, 18)
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