Self-dual double cyclic codes over Z2

A double cyclic code (or emph{DC code}) of length n=k+l over Z2 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.