  We study $\Theta_S-$cyclic codes over the family of rings $A_k.$ We
characterize $\Theta_S-$cyclic codes in terms of their binary images. A family
of Hermitian inner-products is defined and we prove that if a code is
$\Theta_S-$cyclic then its Hermitian dual is also $\Theta_S-$cyclic. Finally,
we give constructions of $\Theta_S-$cyclic codes.
