Multiple choice
The 5-qubit perfect code has 4 stabilizer generators, written as rows of a check matrix [X-part | Z-part] over GF(2) with n = 5. The 4 generators are XZZXI, IXZZX, XIXZZ, ZXIXZ. The number of encoded logical qubits is k = n - rank(check matrix). If Gaussian elimination over GF(2) gives the 4 rows full rank 4, what is k?