General covering-radius conjecture for longest MDS codes

Let $q$ be odd, and let $C$ be a linear MDS code with parameters $[q+1,k]$ over $\mathbb{F}_q$. Its covering radius is denoted by $\rho(C)$.

General covering-radius conjecture. For $2\le k\le q-2$,

$$\rho(C)=q-k.$$

This extends the covering-radius conjecture from projective Reed–Solomon codes to every MDS code of the longest conjecturally possible length $q+1$. It is known in several parameter ranges; the source notes that non-PRS MDS codes exist, so the claim does not follow formally from the projective Reed–Solomon case.