function H = hadamard(n)
%HADAMARD  Hadamard matrix.
%          HADAMARD(N) is a Hadamard matrix of order N, that is,
%          a matrix H with elements 1 or -1 such that H*H' = N*EYE(N).
%          An N-by-N Hadamard matrix with N>2 exists only if REM(N,4) = 0.
%          This function handles only the cases where N, N/12 or N/20
%          is a power of 2.

%          Reference:
%          S.W. Golomb and L.D. Baumert, The search for Hadamard matrices,
%          Amer. Math. Monthly, 70 (1963) pp. 12-17.

%          History:
%          NJH (11/14/91), revised by CBM, 6/24/92,
%          comment lines revised by NJH, August 1993.

[f,e] = log2([n n/12 n/20]);
k = find(f==1/2 & e>0);
if isempty(k)
   error(['N, N/12 or N/20 must be a power of 2.']);
end
e = e(k)-1;

if k == 1        % N = 1 * 2^e;
   H = [1];

elseif k == 2    % N = 12 * 2^e;
   H = [ones(1,12); ones(11,1) ...
        toeplitz([-1 -1 1 -1 -1 -1 1 1 1 -1 1],[-1 1 -1 1 1 1 -1 -1 -1 1 -1])];

elseif k == 3    % N = 20 * 2^e;
   H = [ones(1,20); ones(19,1)   ...
        hankel([-1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1 1], ...
               [1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1])];
end

%  Kronecker product construction.
for i = 1:e
    H = [H  H
         H -H];
end