  It has been shown that good structured codes over non-Abelian groups do
exist. Specifically, we construct codes over the smallest non-Abelian group
$\mathds{D}_6$ and show that the performance of these codes is superior to the
performance of Abelian group codes of the same alphabet size. This promises the
possibility of using non-Abelian codes for multi-terminal settings where the
structure of the code can be exploited to gain performance.
