An Introduction to Linear and Cyclic Codes

Daniel Augot (), Emanuele Betti () and Emmanuela Orsini ()
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Daniel Augot: INRIA Paris-Rocquencourt
Emanuele Betti: University of Florence, Department of Mathematics
Emmanuela Orsini: University of Milan, Department of Mathematics

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 47-68 from Springer

Abstract: Abstract 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.

Keywords: Linear Code; Cyclic Code; Generator Polynomial; Perfect Code; Maximum Distance Separable (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_4

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DOI: 10.1007/978-3-540-93806-4_4

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