Define matrix in MATLAB with 0s and 1s

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 ?

Answer 1

[Pourya Alinezhad]

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.

[Shirish]

The matrix H I am getting is incorrect. I am getting below H

     Columns 1 through 21
        1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     1     0     0     0     1     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     1     1     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     0     0     0     0     0     0     0     0     0     0     0     0     0     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     1     1
             1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1     1
             0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     1
             0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0
             0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0
             1     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

    Columns 22 through 25

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

[Pourya Alinezhad]

so the work is finished... just type :

   z=null(H);