  Let $\Psi_{k,n}$ denote the number of inequivalent binary self-orthogonal
$[n,k]$ codes. We present a method which allows us to compute $\Psi_{k,n}$
explicitly for a moderate $k$ and an arbitrary $n$. Included in this paper are
explicit formulas for $\Psi_{k,n}$ with $k\le 5$.
