  When the environmental disturbace to a quantum system has a wavelength much
larger than the system size, all qubits localized within a small area are under
action of the same error operators. Noiseless subsystem and decoherence free
subspace are known to correct such collective errors. We construct simple
quantum circuits, which implement these collective error correction codes, for
a small number $n$ of physical qubits. A single logical qubit is encoded with
$n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive
relations among the subspaces employed in noiseless subsystem and decoherence
free subspace play essential r\^oles in our implementation. The recursive
relations also show that the number of gates required to encode $m$ logical
qubits increases linearly in $m$.
