|Title||An introduction to linear and cyclic codes.|
|Author(s)|| Daniel Augot, Emanuele Betti, Emmanuela Orsini|
|Type||Book, Chapter in Book, Conference Proceeding|
|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.