Ding et al.'s Bose-distance conjecture for primitive BCH codes

Let $q$ be a prime power, let $m$ and $t$ be positive integers, and let $\mathbf{C}_{(q,q^m-1,q^t+1,1)}$ be the narrow-sense primitive BCH code of length $q^m-1$, designed distance $q^t+1$, and offset $1$. Write $d$ for its minimum distance and $d_B$ for its Bose distance.

Ding et al.'s conjecture. The minimum distance is always equal to the Bose distance:

$$d=d_B=\left\lfloor \frac{q^m-2}{q^{m-t}-1}\right\rfloor+1.$$

The conjecture concerns the exact minimum distance of a broad family of primitive BCH codes and would determine it beyond the cases established in the paper. The source proves $d=q^t+1$ when $m\equiv 0\pmod{pt}$, where $p$ is the characteristic of $\mathbb{F}_q$, but does not resolve the full conjecture.