  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 quantum error correcting code. Fortunately, some errors of
different weights are logically equivalent and the same correction procedure is
applicable to all equivalent errors, thus correcting high-weight errors is
sometimes possible. In this work, we introduce a technique called weight parity
error correction (WPEC) which can correct Pauli error of any weight in some
stabilizer codes provided that the parity of the weight of the error is known.
We show that the technique is applicable to concatenated codes constructed from
the [[7,1,3]] Steane code or the [[23,1,7]] Golay code. We also provide a
fault-tolerant error correction protocol using WPEC for the [[49,1,9]]
concatenated Steane code which can correct up to 3 faults and requires only 2
ancillas.
