A matrix ring description for cyclic convolutional codes
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.
convolutional codes skew polynomial rings cyclic codes forney indices