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{{TEX|done}}{{MSC|94B60}}

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,
$$
0 \mapsto 00 \ ,\ \  1 \mapsto 01 \ ,\ \  2 \mapsto 11 \ ,\ \  3 \mapsto 10 \ .
$$

The map instantiates a [[Gray code]] in dimension 2.

==References==
* Richard E. Blahut, "Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach", Cambridge (2008) ISBN 978-0-521-77194-8 {{ZBL|1147.94001}}