“To perform the error-correction operation for a Stabilizer code, we measure the eigenvalue of each generator of the stabilizer group.”

Set of eigenvalues is the error syndrome. Tells us which error occured.

“The error will always be in 𝒢 since the code uses that error basis, and every operator in 𝒢 is unitary, and therefore invertible. Then we just apply the error operator (or one equivalent to it by multiplication by S) to fix the state.”

“Note that even if the original error that occurred is a nontrivial linear combination of errors in 𝒢, the process of syndrome measurement will project onto one of the basis errors. If the resulting error is not in the correctable set, we will end up in the wrong encoded state, but otherwise, we are in the correct state.”

“A general error acting on the code block can be expanded in terms of Pauli operators. Therefore, we can characterize the efficacy of error correction by considering how well we can protect the encoded state against Pauli operator errors.” link