2-rank preservation for partial geometries from maximal arcs

Let $G$ be a partial geometry with parameters $(s,t,\alpha)$ as in the paper, where $d=2^i\ge 2$ and $d'=2^j\ge 2$, and let $\mathcal{P}$ be a projective plane of order $q=2^{i+j}$. Suppose that $G$ arises from a maximal arc of degree $d$ in $\mathcal{P}$ via the paper's Construction. 2-rank conjecture. The $2$-rank of the $(0,1)$-incidence matrix of $G$ equals the $2$-rank of the $(0,1)$-incidence matrix of $\mathcal{P}$. The conjecture is motivated by the computations reported for the known examples, but its general status is not resolved in the supplied text.