On the structure of convolutional and cyclic convolutional codes

Algebraic convolutional coding theory is considered. It is shown that any convolutional code has a canonical direct decomposition into subcodes and that this decomposition leads in a natural way to a minimal encoder. Considering cyclic convolutional codes, as defined by Piret, an easy application of the general theory yields a canonical direct decomposition into cyclic subcodes, and at the same time a canonical minimal encoder for such codes. A list of pairs admitting completely proper cyclic -convolutional codes is included.