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Question about Hamming Codes

  1. Nov 27, 2004 #1
    I am Writing a paper on ECC for Linear Algebra and I found a nice resource about Hamming Codes. it gives a nice walk through on the way they work and how to construct them... really good.

    I have a problem in a few areas though. the walk through just jumps into some aspects with out explanation and I am getting lost in the shuffle.


    for instance. to warm you up, they give you a nice 3 x 4 binary matrix.

    the basis for the column space was simple, and so was the basis for the Nul space, in this case a basis of the Nul Space is:

    [1] [1]
    [1] [1]
    [1] [0]
    [0] [1]

    that was self evident. however, they completed the Nul space. they added the zero vector, big surprise :-) , but they also added the vector:

    [0]
    [0]
    [1]
    [0]

    I have no idea how they got that vector.
    the Nul space is very important in hamming codes, and I would like to know what is wrong that I can not see where this vector came from.


    thanks for the help.
     
  2. jcsd
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