The nested-clique B-form code distance conjecture

Let $t$ be an odd prime number. Consider the nested clique graph with respect to the permutations in beqrefbpermsd, and let $bmathcal Cd$ be the associated $B$-form code. Its length is the number of coordinates in the construction. Nested-clique B-form code conjecture. The code $bmathcal Cd$ has length $t^2$ and binary distance at least $2t-2$. The conjecture would imply a family of codes whose binary distance grows on the order of the square root of the length, since the construction has length $t^2$; the source states that this remains to be proved or disproved.