  We prove that the class of $\Z_2\Z_2[u]$-linear codes is exactly the class of
$\Z_2$-linear codes with automorphism group of even order. Using this
characterization, we give examples of known codes, e.g. perfect codes, which
has a nontrivial $\Z_2\Z_2[u]$ structure. We also exhibit an example of a
$\Z_2$-linear code which is not $\Z_2\Z_2[u]$-linear. Also, we state that
duality of $\Z_2\Z_2[u]$-linear codes is the same that duality of $\Z_2$-linear
codes.
  Finally, we prove that the class of $\Z_2\Z_4$-linear codes which are also
$\Z_2$-linear is strictly contained in the class of $\Z_2\Z_2[u]$-linear codes.
