cyclic code

Let $C$ be a linear code over a finite field $A$ of block length $n$ . $C$ is called a cyclic code, if for every codeword $c=(c_{1},\ldots,c_{n})$ from $C$ , the word $(c_{n},c_{1},\ldots,c_{n-1})\in A^{n}$ obtained by a right shift of is also a codeword from $C$ .

Sometimes, $C$ is called the $c$ -cyclic code, if $C$ is the smallest cyclic code containing $c$ , or, in other words, $C$ is the linear code generated by $c$ and all codewords obtained by shifts of its .

For example, if $A=\mathbb{F}_{2}$ and $n=3$ , the codewords contained in the $(1,1,0)$ -cyclic code are precisely

(0,0,0),(1,1,0),(0,1,1)\text{ and }(1,0,1).

Trivial examples of cyclic codes are $A^{n}$ itself and the code containing only the zero codeword.

Title	cyclic code
Canonical name	CyclicCode
Date of creation	2013-03-22 15:12:56
Last modified on	2013-03-22 15:12:56
Owner	GrafZahl (9234)
Last modified by	GrafZahl (9234)
Numerical id	6
Author	GrafZahl (9234)
Entry type	Definition
Classification	msc 94B15
Related topic	LinearCode
Related topic	Code