Results 1 to 2 of 2

Math Help - Coding Theory - Parity Check Matrix

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    2

    Coding Theory - Parity Check Matrix

    Hello,

    Problem: Give the parity check matrix H of a [9,6,3] code over GF(7).

    Attempt: Well I know that n=9, k=6, and d=3. GF(7) is looked at like an "alphabet" of elements to choose from, but I am just drawing a blank on the construction of this parity check matrix. I am used to working with fields like GF(2), GF(8), and GF(9) - this one proves to be more difficult...

    Any help would be most appreciated. Thank you for your time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Dec 2008
    Posts
    2
    It is not clear to me can you go the expansion field or not.
    If not, the only code I see here is Reed-Solomon [6,4,3]:
    in GF(7), primitive element is 5, so single error-correcting code with d=3 has generator: (x - 5)(x - 4).
    To reach requested code length you have to expand code. Do you allow to do this?
    Otherwise, just go to expansion GF(49) and then shorten the big code.
    The problem does not say whether I am allowed to expand or not, so I am guessing that I need to find an answer by any means necessary.

    So I would have the identity matrix (6x6) for part of my generator matrix (9x6).

    (I'm trying to derive the generator matrix... then it will be simple for me to convert it to parity check matrix.)

    Any further help regarding the expand route would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Parity-check matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 2nd 2012, 08:07 AM
  2. Coding Theory- help with polynomials
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: May 13th 2011, 11:01 AM
  3. Dimension of a parity check matrix?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 3rd 2010, 09:15 AM
  4. linear code,parity check matrices
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 29th 2010, 06:41 PM
  5. Coding theory question
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 13th 2008, 05:31 PM

Search Tags


/mathhelpforum @mathhelpforum