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Find the largest subset of all binary arrays of length $n$ with $r$ ones which have pairwise distance greater than $m$

Let $\Omega = \left\lbrace x : |x| = r \, \text{for} \, x \in \mathbb{Z}_2^n \right\rbrace$ for $r \in \mathbb{N}$. We want to find the the biggest subset of $\Omega$, $\Gamma = \left\lbrace x \in \...