In this note, we prove that for a subset $\mathcal{F}$ of $\{0,1\}^n$ of density $\frac{1}{8}$, its average pairwise Hamming distance is at least $\frac{n-3}{2}$, with equality attained only by $(n-3)$-dimensional subcubes. This answers a question of Lei Yu, and solves an important open case of a more general question posed by Ahlswede and Katona in 1977.

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