This is almost certainly not the most efficient way of doing it but it seems to work. Will need the statistics and ML toolbox for the randsample function.
numRows = 216;
numCols = 432;
H = zeros(numRows,numCols);
% How many ones are we going to have per column? Between one and three
numOnesPerCol = randi([1,3],[1,numCols]);
% Randomly choose where on each colum these ones are going to be
for col=1:numCols
numOnes = numOnesPerCol(col); % Number of ones in this column
indices = randsample(numRows,numOnes) % Which rows are the ones going to be put
H(indices,col) = 1; % Put the ones in this column
end
