Hamming Code (original) (raw)

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Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology

Alphabetical Index New in MathWorld

• Discrete Mathematics
• Coding Theory

A binary Hamming code of length (with ) is a linear code with parity-check matrix whose columns consist of all nonzero binary vectors of length, each used once (MacWilliams and Sloane 1977). is an 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." FromMathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HammingCode.html

Subject classifications

• Discrete Mathematics
• Coding Theory