In this paper, necessary and sufficient conditions for a cyclic code of arbitrary length over the non-chain rings $Z_{4}+\nu Z_{4}$ for $\nu^{2} \in \{0,1,\nu,2\nu,3\nu,2+\nu,2+3\nu,3+2\nu\}$ to be a reversible cyclic code have been established. Also, conditions for a cyclic code over these non-chain rings to be a reversible complement cyclic code which are necessary as well as sufficient have been determined. Some examples of reversible and reversible complement cyclic codes over these rings have also been presented.

翻译：在本文中，我们建立了任意长度的循环码在非链环$Z_{4}+\nu Z_{4}$上为可逆循环码的充要条件。同时，我们还确定了在这些非链环上，循环码为可逆互补循环码的必要充分条件。此外，我们还介绍了这些环上可逆循环码和可逆互补循环码的一些例子。