Geng et al.'s AMDS conjecture for the dual BCH code

Let $q=3^s$, where $s$ is odd, and let $\mathcal{C}^\perp_{(q,q+1,3,4)}$ denote the dual of the BCH code with these parameters. An AMDS code is an almost maximum-distance-separable code; here the claimed parameters are length $q+1$, dimension $4$, and minimum distance $q-3$.

Geng et al.'s AMDS conjecture. The code $\mathcal{C}^\perp_{(q,q+1,3,4)}$ is an AMDS code with parameters $[q+1,4,q-3]$.

Geng et al. proposed this claim after proving that the corresponding BCH code is AMDS for odd $s$. The conjecture concerns an infinite family of dual BCH codes and remains unresolved in the supplied source.