Equality conjecture for linkage construction bounds

Let $q$ be a prime power, and let $B_q(v_1,v_2,d;k)$ denote the maximum size of a constant-dimension code in a $v_1$-dimensional vector space whose codewords have dimension $k$, minimum subspace distance $d$, and intersect a fixed $v_2$-dimensional subspace in dimension at least $d/2$. Let $A_q(n,d;k)$ denote the maximum size of a constant-dimension code with ambient dimension $n$, codeword dimension $k$, and minimum subspace distance $d$. Equality conjecture for linkage construction bounds. If $v_1\ge v_2+2\ge k+1$ and $k\ge 3$, then

$$B_q(v_1,v_2,2k-2;k)=A_q(v_2,2k-4;k-1).$$

This conjectures that the lower bound produced by the linkage construction is sharp in the indicated parameter range, giving an exact value for $B_q$. The claim is presented as a conjecture based on computational trials and heuristic construction; its resolution is not established in the supplied text.