It is shown that

convolutional codes with unit memory always achieve the largest free distance among all codes of the same rate

and same number

of encoder states, where

is the encoder memory. A unit-memory code with maximal free distance is given at each place where this free distance exceeds that of the best code with

and

relatively prime, for all

and for

. It is shown that the unit-memory codes are byte oriented in such a way as to be attractive for use in concatenated coding systems.