Cyclic linear code: Difference between revisions
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==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
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 be a -linear code. Then the code is cyclic if whenever , for any which simply permutes the coordinates cyclically in the basis .