how to build all binary vectors of length n whose number of its zero elements is m<n?

how to build all binary vectors of length n whose number of its zero elements is m<n?

Answer 1

[Image Analyst]

If you specify m, and want all binary vectors with length longer than m, then there is an infinite number of vectors satisfying that. For example

m = 4;
output = false(1, 7)  % This one has length 7.
output = false(1, 42)  % This one has length 42.

Answer 2

[Roger Stafford]

 N = 0;
 for k = 0:m
   N = N + nchoosek(n,k);
 end
 A = ones(N,n);
 q = 1;
 for k = 1:m
   p = nchoosek(1:n,k);
   for r = 1:size(p,1)
     q = q+1;
     A(q,p(r,:)) = 0;
   end
 end

The n-element rows of array A have all possible combinations of ones and zeros in which there are no more than m zeros. I assumed here that m and n were fixed quantities which you specify.