function T = bintree(L)
% a binary tree on L levels
n = 2^(L) - 1;

global T0 L0 n0
T0 = zeros(n);
L0 = L;
n0 = 1;

subt(1,1);
T = T0;

% order tree properly
sig = lexordtree(T);
sig = invperm(sig);
T1 = T*0;

[nodesi,nodesj]=find(T);
ne = length(nodesi);
for e=1:ne
  i = nodesi(e);
  j = nodesj(e);
  T1(sig(i),sig(j)) = 1;
end
T = T1;


return


function subt(i,l)
global L0 T0 n0
if l<L0
  j1 = n0+1;
  j2 = j1+1;
  n0 = j2;
  T0(i,j1) = 1;
  T0(i,j2) = 1;
  subt(j1,l+1);
  subt(j2,l+1);
end
return