On cyclic DNA codes over ${\mathbb{F}}_2+u{\mathbb{F}}_2+u^2{\mathbb{F}}_2$

In the present paper we study the structure of cyclic DNA codes of even lenght over the ring ${\mathbb{F}}_2+u{\mathbb{F}}_2+u^2{\mathbb{F}}_2$ where $u^3=0$. We investigate two presentations of cyclic codes of even lenght over ${\mathbb{F}}_2+u{\mathbb{F}}_2+u^2{\mathbb{F}}_2$ satisfying the reverse constraint and reverse-complement constraint.