  We report new construction of nine-qubit error-correcting code, which
introduces two new nine-qubit codes and one new three-qubit code. Because both
the new two nine-qubit codes have the normal logical operators, as opposed to
the nine-qubit Shor code, it results in different performance when the three
codes are applied in concatenated quantum error-correction. On the other hand,
one of the two nine-qubit codes has the same stabilizer generators as the
nine-qubit Shor code, they are more suitable for the high-wight bit-flip noise,
and the other code has the different stabilizer generators, which is more
suitable for the high-wight phase-flip noise. This work is enlightening to the
construction of quantum error-correcting codes, and adds more options for
optimizing the performance of quantum error-correction.
