  Consider the metric space $\mathcal{C}$ consisting of the $n$-dimensional
Boolean cube equipped with the Hamming distance. A weak isometry of
$\mathcal{C}$ is a permutation of $\mathcal{C}$ preserving a given subset of
Hamming distances. In \cite{Krasin} Krasin showed that in most cases preserving
a single Hamming distance forces a weak isometry to be an isometry. In this
article we study those weak isometries that are not automatically an isometry,
providing a complete classification of weak isometries of $\mathcal{C}$.
