## cyclic subspace

A subspace $S$ of $V_n(F)$ is a cyclic subspace if whenever

In other words, $S$ is a subspace and for each vector $a \in S$, every cyclic shift of a is also in $S$.

## cyclic code

A linear code $C$ is a cyclic code if $C$ is a cyclic subspace.
Examples:

1. $S={(0000)} \subseteq V_4(Z_2)$
2. $S={(0000),(1111)} \subseteq V_4(Z_2)$
3. $S={(0000),(1111),(1100),(0110),(0011),(1001),(1010),(0101)} \subseteq V_4(Z_2)$

04 November 2014

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