lower bound: | 7 |
upper bound: | 9 |
Construction of a [[52,26,7]] quantum code: [1]: [[52, 26, 7]] quantum code over GF(2^2) ConstructionX using cyclic codes [51,39], [51,38], and auxiliary code [1,1] 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 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0|1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 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 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0|1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 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 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0|1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0|0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0|1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0|1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0|1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0|0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 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 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0|1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 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 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 1 1 0|1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 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 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0|1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 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 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 0|1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 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 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0|0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 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 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 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1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0|1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0|0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0|1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0|0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 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 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0|0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 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 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0|0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 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 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0|0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 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 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 1 0] last modified: 2013-12-09