Fault-tolerant quantum error correction using error weight parities

In quantum error correction using imperfect primitives, errors of high weight arising from a few faults are major concerns since they might not be correctable by the correcting code. Fortunately, some different weights logically equivalent and same procedure is applicable to all errors, thus high-weight sometimes possible. this work, we introduce technique called parity (WPEC) which can correct Pauli any in stabilizer codes provided that known. We show concatenated constructed [[7,1,3]] Steane code or [[23,1,7]] Golay also provide fault-tolerant protocol WPEC for [[49,1,9]] up 3 requires only 2 ancillas.