A minimum storage regenerating (MSR) subspace family of $\mathbb{F}_q^{2m}$ is a set $\mathcal{S}$ of $m$-spaces in $\mathbb{F}_q^{2m}$ such that for any $m$-space $S$ in $\mathcal{S}$ there exists an element in $\mathrm{PGL}(2m, q)$ which maps $S$ to a complement and fixes $\mathcal{S} \setminus \{ S \}$ pointwise. We show that an MSR subspace family of $2$-spaces in $\mathbb{F}_q^4$ has at most size $6$ with equality if and only if it is a particular subset of a Segre variety. This implies that an $(n, n-2, 4)$-MSR code has $n \leq 9$.

翻译：最小存储再生（MSR）子空间族是$\mathbb{F}_q^{2m}$中一组$m$维子空间$\mathcal{S}$，使得对于$\mathcal{S}$中的任意$m$维子空间$S$，存在$\mathrm{PGL}(2m, q)$中的一个元素将$S$映射到补空间，并逐点固定$\mathcal{S} \setminus \{ S \}$。我们证明$\mathbb{F}_q^4$中二维MSR子空间族的尺寸至多为$6$，且当且仅当其是Segre簇的某个特定子集时取等号。这意味着$(n, n-2, 4)$-MSR码满足$n \leq 9$。