Recognition by spectrum for finite simple linear groups of small dimensions over fields of characteristic 2

Two groups are said to be isospectral if they share the same set of element orders. For every finite simple linear group $L$ of dimension $n$ over an arbitrary field of characteristic 2, we prove that any finite group $G$ isospectral to $L$ is isomorphic to an automorphic extension of $L$. An explicit formula is derived for the number of isomorphism classes of finite groups that are isospectral to $L$. This account is a continuation of the second author's previous paper where a similar result was established for finite simple linear groups $L$ in a sufficiently large dimension ($n>26$), and so here we confine ourselves to groups of dimension at most 26.