lower bound: | 10 |
upper bound: | 15 |
Construction of a [[51,11,10]] quantum code: [1]: [[51, 11, 10]] quantum code over GF(2^2) cyclic code of length 51 with generating polynomials [ w*x^49 + x^47 + x^46 + x^45 + w^2*x^44 + x^43 + x^40 + w^2*x^38 + w^2*x^37 + x^34 + w*x^33 + x^32 + w^2*x^31 + w^2*x^29 + x^28 + w*x^26 + w*x^24 + w^2*x^22 + x^20 + 1, w^2*x^49 + w*x^47 + w*x^46 + w*x^45 + x^44 + w*x^43 + w*x^40 + x^38 + x^37 + w*x^34 + w^2*x^33 + w*x^32 + x^31 + x^29 + w*x^28 + w^2*x^26 + w^2*x^24 + x^22 + w*x^20 + w ] 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 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1|0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 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 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0|0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 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 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1|0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 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 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1|0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 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 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1|0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 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 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 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 0 0 0 0 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0 0 1 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1|0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1|0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 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 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 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0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 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 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 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 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 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 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 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 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] last modified: 2006-04-03