Description of Maximal Subsets of a Given Diameter in a Hamming space

We describe all maximal (with respect to cardinality) subsets of a unit $n$-cube $B^n$ that have a given diameter. As a corollary, for an arbitrary number $m$, $1\leq m\leq 2^n$, we find one of the subsets of cardinality $m$ with the minimum possible diameter.