Hamming Code

See: Hamming Encoder, Hamming Decoder, Multiclass Classification Algorithm, Error-Correcting Code, Linear Code, Binary Linear Code, Bit Error, Hamming Distance, Parity Code.

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References

2009

• http://en.wikipedia.org/wiki/Hamming_code
  • In telecommunication, a Hamming code is a linear error-correcting code named after its inventor, Richard Hamming. Hamming codes can detect up to two simultaneous bit errors, and correct single-bit errors; thus, reliable communication is possible when the Hamming distance between the transmitted and received bit patterns is less than or equal to one. By contrast, the simple parity code cannot correct errors, and can only detect an odd number of errors.
  • In mathematical terms, Hamming codes are a class of binary linear codes. For each integer [math]\displaystyle{ m\gt 2 }[/math] there is a code with [math]\displaystyle{ m }[/math] parity bits and [math]\displaystyle{ 2^m-m-1 }[/math] data bits. The parity-check matrix of a Hamming code is constructed by listing all columns of length [math]\displaystyle{ m }[/math] that are pairwise independent.
  • Because of the simplicity of Hamming codes, they are widely used in computer memory (RAM). In particular, a single-error-correcting and double-error-detecting variant commonly referred to as SECDED.

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