Cyclic linear code

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 $w\in W$, $\sigma .w\in W$ for any $\sigma$ which simply permutes the coordinates cyclically in the basis $X$.