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Math Help - self orthogonality with codes

  1. #1
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    self orthogonality with codes

    Hello,
    I'm at a loss when it comes to the next step here
    I've got the question:
    Let C be the [6; 3] binary code with generator matrix
    G =
    1 1 0 0 0 0
    0 1 1 0 0 0
    1 1 1 1 1 1

    Is C self-orthogonal? Do the codewords whose weights are divisible by
    four form a subcode of C? Justify your answers.


    the generator for the dual code, is the parity matrix for the code C
    and a code C is self-orthgonal if C \subseteq C^\perp
    and if G=[I_k|A] is a generator matrix for the [n,k] code C in standard form then H=[-A^T|I_{n-k}] is a parity check matrix for C

    from this I took the matrix and got
    G=
    1 0 0 1 1 1
    0 1 0 1 1 1
    0 0 1 1 1 1
    by row operations
    then I get
    H=C^\perp =
    1 1 1 1 0 0
    1 1 1 0 1 0
    1 1 1 0 0 1

    I don't know what to do from here to show C \subseteq C^\perp or that it's not the case

    I'm also unsure of what to do about the second part of the question, where it asks if the codewords of weight divisible by 4 form a subcode


    edit:
    ok so I know it's not the case
    C is not self orthogonal, and the codewords of weight divisible by 4 are not a subcode of C
    how do I prove this?
    Last edited by jbpellerin; February 17th 2010 at 05:43 PM. Reason: additional info
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