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    function [S,count] = D_Symbol_Set
% provide the smallest delta sybobl set for exhaustive search
% by Jinfeng Du
% 2005-04-22

j = sqrt(-1);
count = 1; % the number of different delta S without those on the coordinates

S = [-6; 6];
interval = [-6 -4 -2 0 2 4 6];
index = 0;
for m = interval
    for n = interval
        for k = interval
            for l= interval
                
                if(m^2+n^2 ~= 0 && k^2+l^2 ~= 0)                
                    newS = [m+n*j;k+l*j];  
                    keep_this = 1;
                                   
                    for p = 1:count
                        % Test the proportionality
                       Div = S(:,p)./newS;
                       if(Div(1) == Div(2)) % if new_delta_s=k delta_s with k>1 dont take
                          if(abs(Div(1)) < 1)
                              keep_this = abs(Div(1));
                              index=p; %replace S(:,index) by newS
                          else
                              keep_this = 0;
                              p = count; % terminate this loop
                          end
                       end
                    end
                    
                    if(keep_this)
                       if(keep_this < 1)
                          S(:,index) = newS;
                       else
                          count = count+1;
                          S = [S , newS];
                       end
                    end
                end
                
            end
        end
    end
end

B=[0 0 0 0 0 0 0 0 2 2+2*j 2+4*j 2+6*j 4+2*j 4+6*j 6+2*j 6+4*j;2 2+2*j 2+4*j 2+6*j 4+2*j 4+6*j 6+2*j 6+4*j 0 0 0 0 0 0 0 0];

S = [S , B];
count = count + length(B(1,:));