Glossary

Parity Check: It can be seen in the second line that one can think of $Z_1 \otimes Z_2$ as measuring the parity of the two physical qubits. If the parity is 0 then the measurement outcome is $(+1)$; if the parity is 1 then the measurement outcome is $(-1)$.

Code Distance: This distance of a code is the minimum numbers of errors that will change one codeword to another. Alternatively, the distance of a code is the minimum number of errors that will go undetected.

Abelian Group: A group in which the result of applying the group operation to two group elements does not depend on the order in which they are written i.e $g_1 \cdot g_2 = g_2 \cdot g_1$.

Anti-Hermitian Stabilizers: If $\tilde{P} \in \mathcal{P}_n$ is not Hermitian, such that $\tilde{P}^\dagger \neq \tilde{P}$, the there exists a $Q \in \mathcal{P}_n$, such that $Q^\dagger = Q$, where $Q=(\pm i) \tilde{P}$. Given the complex phase does not effect the measurement outcomes, one can just measure $Q$ using this method in place of $\tilde{P}$.