A link between quasi-cyclic codes and convolutional codes

Given a quasi-cyclic code with minimum Hamming distance d, a set of convolutional codes is derived with free distance equal to d. It is shown that an increase in the rate of these codes results in a decrease in the memory length. The connection between these codes is illustrated with several well-known quasi-cyclic codes. The free distance of some partial unit memory convolutional codes can be determined using the results in this correspondence.