The s-independence number of the exact-r-distance graph on the hypercube is asymptotically Θ(2^n / n^{r/2}) for fixed s ≥ 2 and even r ≥ 2.
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Forbidding Exactly One Hamming Distance
The s-independence number of the exact-r-distance graph on the hypercube is asymptotically Θ(2^n / n^{r/2}) for fixed s ≥ 2 and even r ≥ 2.