  Multi-valued quantum systems can store more information than binary ones for
a given number of quantum states. For reliable operation of multi-valued
quantum systems, error correction is mandated. In this paper, we propose a
5-qutrit quantum error-correcting code and provide its stabilizer formulation.
Since 5 qutrits are necessary to correct a single error, our proposed code is
optimal in the number of qutrits. We prove that the error model considered in
this paper spans the entire $(3 \times 3)$ operator space. Therefore, our
proposed code can correct any single error on the codeword. This code
outperforms the previous 9-qutrit code in (i) the number of qutrits required
for encoding, (ii) our code can correct any arbitrary $(3 \times 3)$ error,
(ii) our code can readily correct bit errors in a single step as opposed to the
two-step correction used previously, and (iii) phase error correction does not
require correcting individual subspaces.
