  It is proved in a reference (Fan, Lin, IEEE TIT, vol.67, pp.5016-5025) that
the self-dual (LCD respectively) dihedral codes over a finite field~$F$ with
${|F|=q}$ are asymptotically good if $q$ is even (odd respectively). In this
paper, we investigate the algebraic property and the asymptotic property of
conta-dihedral codes over $F$, and show that: if $q$ is even or $4\,|\,(q-1)$,
then the self-dual consta-dihedral codes are asymptotically good; otherwise,
the LCD consta-dihedral codes are asymptotically good. And, with the help of a
technique developed in this paper, some errors in the reference mentioned above
are corrected.
