Asymptotic Lower Bound on the Free Distance of Constant Linear Convolutional Codes with Rate $1/n_0$

A new asymptotic lower bound is obtained for the ratio of the free distance to the constraint length in the class of constant binary linear convolutional codes with rates of the form $1/n_0$. For all $n_0\ge 3$ the new bound is an improvement on the Neumann bound, but does not attain the Costello bound, which has been proved for the class of time-dependent linear convolutional codes.