lower bound: | 12 |
upper bound: | 17 |
Construction of a [[54,8,12]] quantum code: [1]: [[54, 8, 12]] quantum code over GF(2^2) Code found by Petr Lisonek and Vijaykumar Singh Construction from a stored generator matrix stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0|0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0|0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0|0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0|1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0|0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0|0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0|0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0|1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0|1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0|0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0|0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0|1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0|0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0|0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0|0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0|0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0|1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0|1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0|1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0|1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0|1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0|1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0|1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0|1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0|1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0|1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0|0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0|1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0|0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0|0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0|1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0|0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0|0 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0|0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0|0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0|0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0|1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0|0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0|0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0|1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0|0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0|1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0|0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0|1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 0] last modified: 2013-11-14