The second and third largest coset leader conjecture for characteristic-two BCH codes

Let $q$ be a power of $2$ and let $n=q^m+1$, with the quantities $\delta_2$ and $\delta_3$ defined as in the preceding cases for even $m$. Second and third largest coset leader conjecture. If $\delta_2$ and $\delta_3$ are given as above, then $\delta_2$ and $\delta_3$ are the second and third largest coset leaders, respectively. These formulas are conjectured for BCH codes over fields of characteristic two, following the analogous verified results and the computations reported in the paper; the conjecture remains unresolved in the supplied text.