← 研踪 PaperTrailarXiv:2610.40486 · v1
Average pairwise Hamming distance of a subset in a hypercube
首次提交 2026-10-30 01:15
版本更新 2026-10-30 01:15
雷达观测 2026-10-30 13:28
摘要
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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Average pairwise Hamming distance of a subset in a hypercube
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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