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Thread: 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 $\displaystyle C \subseteq C^\perp$
    and if $\displaystyle G=[I_k|A]$ is a generator matrix for the [n,k] code C in standard form then $\displaystyle H=[-A^T|I_{n-k}]$ 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
    $\displaystyle H=C^\perp =$
    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 $\displaystyle C \subseteq C^\perp$ 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; Feb 17th 2010 at 04:43 PM. Reason: additional info
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