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Hamming Code

A binary Hamming code H_r of length n=2^r-1 (with r>=2) is a linear code with parity-check matrix H whose columns consist of all nonzero binary vectors of length r, each used once (MacWilliams and Sloane 1977). H_r is an (n=2^r-1,k=2^r-1-r,d=3) code. Hamming codes are perfect single error-correcting codes.

See also

Error-Correcting Code, Hamming Distance, Hamming Graph, Perfect Code

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References

MacWilliams, F. J. and Sloane, N. J. A. The Theory of Error-Correcting Codes. Amsterdam, Netherlands: North-Holland, 1977.

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Hamming Code

Cite this as:

Weisstein, Eric W. "Hamming Code." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HammingCode.html

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