Construction of Cyclic Codes over $\mathbb{F}_2+u\mathbb{F}_2$ for DNA Computing

We construct codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ with $u^2=0$. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint and avoid the secondary structure. they are derived from the cyclic complement reversible codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$. We also construct an infinite family of BCH DNA codes.