Difference between revisions of "Gray map"
From Encyclopedia of Mathematics
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| − | 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, | + | 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, |
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0 \mapsto 00 \ ,\ \ 1 \mapsto 01 \ ,\ \ 2 \mapsto 11 \ ,\ \ 3 \mapsto 10 \ . | 0 \mapsto 00 \ ,\ \ 1 \mapsto 01 \ ,\ \ 2 \mapsto 11 \ ,\ \ 3 \mapsto 10 \ . | ||
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==References== | ==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}} | + | * Richard E. Blahut, "Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach", Cambridge (2008) {{ISBN|978-0-521-77194-8}} {{ZBL|1147.94001}} |
Latest revision as of 09:29, 28 October 2023
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=51488
Gray map. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Gray_map&oldid=51488