Gray Map

The Gray map from to binary pairs is the bijection , , , and , extended coordinatewise to words over . It takes a length- quaternary code to a length- binary code. Its binary image need not be a linear code, even when the quaternary code is linear over the ring .

The modified binary Preparata-like codes of Hammons et al. (1994) are Gray images of linear codes over .

See also

Code, Gray Code, Preparata Code

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References

Hammons, A. R., Jr.; Kumar, P. V.; Calderbank, A. R.; Sloane, N. J. A.; and Solé, P. "The

-Linearity of Kerdock, Preparata, Goethals, and Related Codes." IEEE Trans. Inform. Th. 40, 301-319, 1994. https://doi.org/10.1109/18.312154.

Cite this as:

Weisstein, Eric W. "Gray Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GrayMap.html

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