---

＜電子ブック＞
Error-Correcting Linear Codes : Classification by Isometry and Applications / by Anton Betten, Michael Braun, Harald Fripertinger, Adalbert Kerber, Axel Kohnert, Alfred Wassermann
(Algorithms and Computation in Mathematics ; 18)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XXIX, 798 p : online resource
著者標目	*Betten, Anton author Braun, Michael author Fripertinger, Harald author Kerber, Adalbert author Kohnert, Axel author Wassermann, Alfred author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algorithms LCSH:Coding theory LCSH:Information theory LCSH:Signal processing LCSH:Discrete mathematics FREE:Algebra FREE:Algorithms FREE:Coding and Information Theory FREE:Signal, Speech and Image Processing FREE:Discrete Mathematics
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/3-540-31703-1

 類似資料