lower bound: | 10 |
upper bound: | 13 |
Construction of a [[53,17,10]] quantum code: [1]: [[53, 17, 10]] quantum code over GF(2^2) ConstructionXX using cyclic codes [51,35], [51,34], [51,34], and auxiliary codes [1,1], [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 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0|0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 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 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 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 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 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 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 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 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0|0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 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 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 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 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 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 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1] [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 1 0 0 0 0 0 1 0 1 1 1 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 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 0 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 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 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 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 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 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 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 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0] last modified: 2013-12-09