Here's some code that generalizes the example for any n (size of original matrix), except this expands the matrix to size n^2-by-n^2. (It's not clear (to me) how the process would work for n > 2 in order to generate a matrix of size 2n-by-2n.)
original = [1 2; 3 4];
n = size(original,1);
newmatrix = zeros(n^2);
for ii = 1:n
rows = n*(ii-1)+(1:n);
for jj = 1:n
cols = n*(jj-1)+(1:n);
temp = original;
temp(ii,jj) = 0;
newmatrix(rows,cols) = bitxor(original(ii,jj),temp);
end
end
newmatrix
And to get the original matrix back:
idx = 1+(n+1)*(0:n-1);
neworiginal = newmatrix(idx,idx)
