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Multiplication of two matrices ? one in GF(2) other in R

  1. Oct 28, 2011 #1
    1. The problem statement, all variables and given/known data
    H is a nxn matrix with elements in {0,1}
    G is a nxn matrix with elements in GF(2)
    m is a nx1 vector with elements in GF(2).
    How can we perceive the output of
    HGm where Gm multiplication is in GF(2) and H multiplication is a normal real multiplication.
    Actually I want to combine HG transformation into one P transformation. How can I multiply two matrices while elements in one is in GF(2) and other is in R ?
    (We can also restrict the entries in H to be one of 0 and 1 but the output can be in R).


    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 28, 2011 #2

    Deveno

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    Science Advisor

    the entries in the vector Gm will still be in GF(2) = {0,1}.

    so basically the vector Gm acts as a "choice function" picking out which columns of H get summed in the ouput, which will be a real-valued vector.

    it makes more sense to do it this way, than to imagine what "HG" means (in this case G acts in a more complicated way, which is then subjected to another selection via m).

    in general, (HG)m and H(Gm) won't yield the same results:

    [a b]([1 0][1])
    [c d]([1 1][1]) =

    [a b][1]
    [c d][0], which is (a,c)

    ([a b][1 0])[1]
    ([c d][1 1])[1] =

    [a+b b][1]
    [c+d d][1] = (a+2b,c+2d), which is only equal to the first mod 2.
     
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