  Error correction is of utmost necessity for large-scale quantum computing.
Quantum error correcting codes can be degenerate, if more than one type of
error can map the input state to the same error state. In this paper, we
propose a 6-qubit degenerate CSS code. We show that our proposed code can
correct a single bit flip error, but arbitrarily many phase flip errors
occurring on the codeword. Furthermore, it follows from a bound on CSS codes
that the proposed code is the minimal binary CSS code which can encode a single
qubit of information. We also perform a comparative study of the gate count
required for a fault tolerant decomposition of the error correction circuit for
the proposed code, with that for the existing 9-qubit, 7-qubit and 5-qubit
binary QEC codes. Our results show, on an average over the different
technologies a savings of 98.14% in the gate count for the proposed code over
that for the 5-qubit code. Significant improvement of around 50% in gate count
is also obtained when compared to those for the 9-qubit and 7-qubit codes.
