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I have never use MATLAB before but I have to do one operation that deal with matrix of 25(row) x 25(col). So I don't want to do this by hand. So I have to use matlab.

I want to define matrix in MATLAB of GF(2) (the Galois field of order 2 is a mathematical structure called a field that provides a formal definition of arithmetic modulo two) .

Following is my matrix

1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1

Now I want to find the NULL SPACE of the above matrix. I know the NULL Space of the above matrix is

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

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

How to do this operation in MATLAB? In short how to define the matrix with GF(2) and also to find the NULL SPACE of that matrix ?

Pourya Alinezhad
on 2 Mar 2014

Edited: Pourya Alinezhad
on 2 Mar 2014

define a vector as :

a= [1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ];

you can see the matrix raw's are circularly shifted copies of this vector

for i=1:25

H(i,:)=circshift(a,[0 i-2]);

end

the H matrix is just the one you need... then use a subspace base decomposition method to find the Null space... for example egn() or svd() functions can help u... i am an electrical and communications eng and i know what u exactly need... hope to be helpful.

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