Talk:Cyclic code

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Telecommunications

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Not cryptography

This article is not cryptoraphy related, it is about coding schemes for robust telecommunications.

I have a degree in Management Information Systems. I am trying to learn what a cyclic code is. This article has left an emotional impression, but I have not learned what I came here seeking. I am leaving to go elsewhere on the Internet to learn what a cyclic code is.

[email protected]

Irreducible code

In the section "Algebraic structure", Wikipeida said:

An irreducible code is a cyclic code in which the code, as an ideal, is minimal in R, so that its generator is an irreducible polynomial.

But irreducible polynomial generate maximal ideal.

From J.H.van Lint's book "Introduction to Coding Theory" page 83, (6.1.6):

The cyclic code generated by $f_{i}(x)$ is called a maximal cyclic code(since it is a maximal ideal) and denote by $M_{i}^{+}$ . The code generated by ${\frac {x^{n}-1}{f_{i}(x)}}$ is called a minimal cyclic code and denoted by $M_{i}^{-}$ . Minimal cyclic codes are also called irreducible cyclic codes.

--Zxl.gzhu (talk) 09:33, 10 April 2010 (UTC)[reply]