  We characterize the structure of 2-quasi-cyclic codes over a finite field F
by the so-called Goursat Lemma. With the characterization, we exhibit a
necessary and sufficient condition for a 2-quasi-cyclic code being a dihedral
code. And we obtain a necessary and sufficient condition for a self-dual
2-quasi-cyclic code being a dihedral code (if charF = 2), or a consta-dihedral
code (if charF odd). As a consequence, any self-dual 2-quasi-cyclic code
generated by one element must be (consta-)dihedral. In particular, any
self-dual double circulant code must be (consta-)dihedral. Also, we show a
necessary and sufficient condition that the three classes (the self-dual double
circulant codes, the self-dual 2-quasi-cyclic codes, and the self-dual
(consta-)dihedral codes) are coincide each other.
