On the structure of rate1/nconvolutional codes

We show what choice there is in assigning output digits to transitions of a binary rate
1/n
code trellis so that the latter will correspond to a convolutional code. We then prove that in any rate
\frac{1}{2}
noncatastrophic code of constraint length
\upsilon
each binary sequence of length
2j
(1 \leq j \leq \upsilon - 1)
is associated with exactly
2^{\upsilon -j -1}
distinct paths
j
branches long. As a consequence of the above properties nondegenerate codes with branch complementarity are fully determined by the topological relationship of the trellis transitions associated with output pairs 00. Finally, we derive a new upper bound on free distance of rate
1/n
convolutional codes and use our results to determine the length of the largest input sequence that can conceivably result in an output whose weight is