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

The spectrum of a finite group is the set of its element orders. For every finite simple linear group $L=L_n(2^k)$, where $11\le n\le18$ or $n>24$, we describe finite groups having the same spectrum as $L$, prove that the number of pairwise nonisomorphic groups with this property is finite, and derive an explicit formula for calculating this number.