 |
 |
|
|
| HAL: inria-00550061, version 1 |
| DOI: 10.1007/978-3-540-93806-4_4 |
| See detailed view |  BibTeX,EndNote,... |
 |
| Journal of Symbolic Computation (2009) 47-68 |
|
|
|
|
| An introduction to linear and cyclic codes |
|
|
| Daniel Augot 1Emmanuela Orsini 2 |
|
|
| (2009) |
|
|
|
| Our purpose is to recall some basic aspects about linear and cyclic codes. We first briefly describe the role of error-correcting codes in communication. To do this we introduce, with examples, the concept of linear codes and their parameters, in particular the Hamming distance. A fundamental subclass of linear codes is given by cyclic codes, that enjoy a very interesting algebraic structure. In fact, cyclic codes can be viewed as ideals in a residue classes ring of univariate polynomials. BCH codes are the most studied family of cyclic codes, for which some efficient decoding algorithms are known, as the method of Sugiyama. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | SECRET (INRIA Rocquencourt) |
|
|
|
INRIA |
|
|
| 2: | Department of Mathematics "Federigo Enriques |
|
|
|
Università degli studi di Milano |
|
|
| 3: | Dipartimento di Matematica "Ulisse Dini" |
|
|
|
University of Firenze |
|
|
|
|
|
|
|
|
|
| Domain | : | Computer Science/Information Theory and Coding Mathematics/Information Theory |
|
|
| coding theory – cyclic codes |
|
|
|
| Attached file list to this document: | |||||
|
|||||
|
|
|
| inria-00550061, version 1 | |
| http://hal.inria.fr/inria-00550061 | |
| oai:hal.inria.fr:inria-00550061 | |
| From: Daniel Augot | |
| Submitted on: Thursday, 23 December 2010 13:21:03 | |
| Updated on: Tuesday, 30 October 2012 09:34:48 | |
