# Gray map

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 94B60 [MSN][ZBL]

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

**How to Cite This Entry:**

Gray map.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Gray_map&oldid=54168