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The above binary representation and [[symplectic algebra]] are useful in making
the relation between classical linear [[error correction]] and [[quantum error correction]] more explicit.
By comparing quantum error correcting codes in this language to [[symplectic vector space|symplectic vector spaces]], we can see the following. A [[Symplectic_vector_space#Subspaces|symplectic]] subspace corresponds to a [[direct sum]] of Pauli algebras (i.e., encoded qubits), while an [[Symplectic_vector_space#Subspaces|isotropic]] subspace corresponds to a set of stabilizers.
==Example of a stabilizer code==
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