  In this paper, we study convolutional codes with a specific cyclic structure.
By definition, these codes are left ideals in a certain skew polynomial ring.
Using that the skew polynomial ring is isomorphic to a matrix ring we can
describe the algebraic parameters of the codes in a more accessible way. We
show that the existence of such codes with given algebraic parameters can be
reduced to the solvability of a modified rook problem. It is our strong belief
that the rook problem is always solvable, and we present solutions in
particular cases.
