= Symplectic representation of a stabilizer code
A <stabilizer group> with $r$ independent generators maps injectively to an r-dimensional isotropic subspace of the <binary symplectic space of Pauli labels>. For generator rows $(A\mid B)$, commutation is $AB^T+BA^T=0$ over $\mathbb F_2$. Its <stabilizer subspace> has dimension $2^{n-r}$. The labels of the <centralizer of a stabilizer group> form $L^\perp$; labels in $L^\perp\setminus L$ act as nontrivial logical Pauli operators.
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