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Math Help - Hamming Code, Parity Matrix

  1. #1
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    Hamming Code, Parity Matrix

    Have an exam tomorrow. Pretty sure a question like this will be on it. Am a bit lost on this one.

    Any help greatly appreciated. Thanks!
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  2. #2
    MHF Contributor chisigma's Avatar
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    An Hamming (n,k) code is the set of all n-simbols binary word that satisfy the relation...

     \overline{z}= \overline {x} \cdot H= \overline {0} (1)

    ... where...

    a) \overline {x} is a n bit row vector

    b) \overline {z} is a n-k bit column vector called symdrome

    c) \overline {0} is the n-k bit 'null vector'

    d) H is the n x k bit 'parity check' matrix

    An example of parity 7 x 4 Hamming parity check matrix is the following...

     H = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 1 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1\\ 1 & 0 & 1 \end{bmatrix}

    A 7 x 4 Hamming code can correct any single error that occurred in a 7 bits transmitted word...

    Kind regards

    \chi \sigma
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