# Gray map

A map from $\mathbf{Z}_4$ to $\mathbf{F}_2^2$, extended in the obvious way to $\mathbf{Z}_4^n$ and $\mathbf{F}_2^n$, which maps Lee distance to Hamming distance. Explicitly, $$0 \mapsto 00 \ ,\ \ 1 \mapsto 01 \ ,\ \ 2 \mapsto 11 \ ,\ \ 3 \mapsto 10 \ .$$