lower bound: | 7 |
upper bound: | 8 |
Construction of a [[31,9,7]] quantum code: [1]: [[31, 9, 7]] quantum code over GF(2^2) ConstructionX using quasicyclic codes [30,11], [30,10], and auxiliary code [1,1] stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0|1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0|0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0|1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0|1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0|0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0|1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0|0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0|1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0|1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0|0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0|0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0|1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0|0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0|1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 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 0 1 0 1 1 0|0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1] [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 1 1 1 0 0|1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 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 1 1 1 0|0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 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 1 0 0 0 1 0 1 1 1 0 0 0 0|1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 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 1 0 0 0 1 0 1 1 1 0 0 0|0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 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 1 0 0 0 1 0 1 1 1 0 0|1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 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 1 0 0 0 1 0 1 1 1 0|1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 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 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1] last modified: 2020-08-22