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An <math>[n,k]</math> '''stabilizer code''' is a [[linear subspace|subspace]] <math>V_S</math> of the Hilbert space of n [[qubit|qubits]] <math>(\mathbb{C}^2)^{\otimes n}</math>, which is [[Group_action#Orbits_and_stabilizers|stabilized]] by an [[abelian group|abelian]] [[subgroup]] <math>S</math> of the [[Pauli group]] on n qubits <math>G_n</math> such that <math>-I\notin S</math> and <math>S</math> has <math>n-k</math> independent generators, <math>S=\langle g_1,\ldots,g_{n-k}\rangle</math>. These conditions are required so that the vector space stabilized is non-trivial. Denote this code <math>C(S)</math>.
==References==
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