cyclic code

Let C be a linear codeMathworldPlanetmath over a finite field A of block length n. C is called a cyclic codeMathworldPlanetmath, if for every codeword c=(c1,,cn) from C, the word (cn,c1,,cn-1)An 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=𝔽2 and n=3, the codewords contained in the (1,1,0)-cyclic code are precisely

(0,0,0),(1,1,0),(0,1,1) and (1,0,1).

Trivial examples of cyclic codes are An 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