  For a random quasi-abelian code of rate $r$, it is shown that the GV-bound is
a threshold point: if $r$ is less than the GV-bound at $\delta$, then the
probability of the relative distance of the random code being greater than
$\delta$ is almost 1; whereas, if $r$ is bigger than the GV-bound at $\delta$,
then the probability is almost 0. As a consequence, there exist many
asymptotically good quasi-abelian codes with any parameters attaining the
GV-bound.
