Cyclic linear code: Difference between revisions

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{{linear code property}}
{{linear code property}}
{{semibasic nongt def}}


==Definition==
==Definition==


Let <math>(V,X,W)</math> be a <math>(n,k,q)</math>-linear code. Then the code is cyclic if whenever <math>w \in W</math>, <math>\sigma.w \in W</math> for any <math>\sigma<math> which simply permutes the coordinates cyclically in the basis <math>X</math>.
Let <math>(V,X,W)</math> be a <math>(n,k,q)</math>-linear code. Then the code is cyclic if whenever <math>w \in W</math>, <math>\sigma.w \in W</math> for any <math>\sigma</math> which simply permutes the coordinates cyclically in the basis <math>X</math>.

Revision as of 08:17, 6 July 2007

Template:Linear code property

This article is about a standard (though not very rudimentary) definition in an area related to, but not strictly part of, group theory

Definition

Let (V,X,W) be a (n,k,q)-linear code. Then the code is cyclic if whenever wW, σ.wW for any σ which simply permutes the coordinates cyclically in the basis X.