  Quantum convolutional codes can be used to protect a sequence of qubits of
arbitrary length against decoherence. We introduce two new families of quantum
convolutional codes. Our construction is based on an algebraic method which
allows to construct classical convolutional codes from block codes, in
particular BCH codes. These codes have the property that they contain their
Euclidean, respectively Hermitian, dual codes. Hence, they can be used to
define quantum convolutional codes by the stabilizer code construction. We
compute BCH-like bounds on the free distances which can be controlled as in the
case of block codes, and establish that the codes have non-catastrophic
encoders.
