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Generating Walsh-Hadamard codes from Hadamard matrix is much easier. Please look at the following matrix:
1 1
1 0
The next Hadamard matrix would be a 4×4 one being generated by putting the above matrix instead of each of the elements of it. But for the zero elements, you would have to change ones to zeros and zeros to ones. Look:
1 1 1 1
1 0 1 0
1 1 0 0
1 0 0 1
The above matrice is composed of for matrices as depicted above and shown below:
1 1 – 1 1
1 0 – 1 0
1 1 – 0 0
1 0 – 0 1
I hope the explanation is clear. Please compare the two matrices to find the relation. Now every row or column of the above matrices is a code for one user.
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