  Several new families of multi-memory classical convolutional
Bose-Chaudhuri-Hocquenghem (BCH) codes as well as families of unit-memory
quantum convolutional codes are constructed in this paper. Our unit-memory
classical and quantum convolutional codes are optimal in the sense that they
attain the classical (quantum) generalized Singleton bound. The constructions
presented in this paper are performed algebraically and not by computational
search.
