  Let $A_2(n,d)$ be the maximum size of a binary code of length $n$ and minimum
distance $d$. In this paper we present the following new lower bounds:
$A_2(18,4) \ge 5632$, $A_2(21,4) \ge 40960$, $A_2(22,4) \ge 81920$, $A_2(23,4)
\ge 163840$, $A_2(24,4) \ge 327680$, $A_2(24,10) \ge 136$, and $A_2(25,6) \ge
17920$. The new lower bounds are a result of a systematic computer search over
transitive permutation groups.
