A double cyclic code (or \emph{DC code}) of length $n=k+l$ over $\mathbb{Z}_2$ is a binary linear code, where any cyclic shift of the first $k$ coordinates and the last $l$ coordinates of a codeword is also a codeword. In this paper, we study the relationship between separability and self-duality of these codes. Also, we obtain the shadow code by determining the generator polynomials of the doubly even subcode of the self-dual code. Manuscript profile