%file name: hammda.m
%Written by Dr. James S. Kang, Cal Poly Pomona.
%Calculate the message u for the given received vector r 
%when Hamming code is used.
%r = received vector such as [1 1 0 1 0 0 1].
%To run the program, try
% >>hammda([1 1 0 1 0 0 1])  <Enter>
function[H,G,u] = hammda(r)
n=size(r,2); %n = length of r.
m=ceil(log(n)/log(2));
k=n-m;
Im=eye(m);
Q=zeros(m,k);
nc = 0; %nc = number of columns in Q matrix.
count=0; 
d=zeros(m)';
while nc < k
   count=count+1;
   b=dec2bin(count);
   if sum(b)>1
      nc=nc+1;
      s=size(b,1);
      if s<m
	 for j=1:s d(m-s+j)=b(j); end
	 for j=1:m b(j)=d(j); end
      end
      Q(:,nc)=b;
   end
end
H=[Q Im];
Ik=eye(k);
G=[Ik Q'];
disp('Generator Matrix G = ');
disp(G);
disp('The received vector r = ');
disp(r);
sy=rem(r*H',2);
disp('The syndrome = ');
disp(sy)
for i=1:n
   z=0;
   for j=1:m 
      if sy(j) ~= H(j,i) z=z+1; end
   end
   if z==0 
      if r(i) == 1 v(i) = 0; else v(i)=1; end
   else v(i)=r(i); 
   end
end      
disp('The most likely transmitted codeword v = ');
disp(v);
for i=1:k
   u(i)=v(i);
end
disp('The most likely transmitted message u = ');
disp(u);