The MDS probability convergence conjecture

Let $C$ be a linear $[n,k]$ code chosen uniformly at random over a field $\mathbb{F}_q$, where $n,q\to\infty$. The property MDS means that the minimum distance of $C$ is $n-k+1$.

MDS probability convergence conjecture. If

$$\frac{1}{q}\binom{n}{k}\to\lambda\in(0,\infty),$$

then

$$P(C\text{ is MDS})\to e^{-\lambda}.$$

The source notes that this extends the known asymptotic result beyond the regime $k/n\to0$, and leaves the assertion open while providing numerical evidence for the case $n=2k$.