Short binary convolutional codes with maximal free distance for rates 2/3 and 3/4 (Corresp.)

A search procedure is developed to find good short binary
(N,N - 1)
convolutional codes. It uses simple rules to discard from the complete ensemble of codes a large fraction whose free distance
d_{free}
either cannot achieve the maximum value or is equal to
d_{free}
of some code in the remaining set. Farther, the search among the remaining codes is started in a subset in which we expect the possibility of finding codes with large values of
d_{free}
to be good. A number of short, optimum (in the sense of maximizing
d_{free}
), rate-2/3 and 3/4 codes found by the search procedure are listed.