A strengthened asymptotic Gilbert bound for convolutional codes (Corresp.)

The usual statement of the Gilbert bound is an assertion that at least one member of a given ensemble of codes satisfies a minimum distance criterion. This result is strengthened by showing that for sufficiently large constraint lengths, an arbitrarily large fraction of the ensemble of codes have minimum distance exceeding the usual asymptotic Gilbert bound. New asymptotic bounds are derived for the nonbinary case.