lower bound: | 9 |
upper bound: | 12 |
Construction of a [[51,19,9]] quantum code: [1]: [[51, 19, 9]] quantum code over GF(2^2) cyclic code of length 51 with generating polynomials [ w*x^50 + w*x^47 + w^2*x^46 + x^45 + w*x^44 + x^42 + x^41 + x^38 + w^2*x^36 + w^2*x^34 + x^33 + x^31 + x^27 + w^2*x^26 + w*x^25 + w^2*x^24 + w*x^23 + w^2*x^22 + w*x^21 + w^2*x^20 + w*x^19 + w^2*x^18 + w*x^16 + 1, w^2*x^50 + w^2*x^47 + x^46 + w*x^45 + w^2*x^44 + w*x^42 + w*x^41 + w*x^38 + x^36 + x^34 + w*x^33 + w*x^31 + w*x^27 + x^26 + w^2*x^25 + x^24 + w^2*x^23 + x^22 + w^2*x^21 + x^20 + w^2*x^19 + x^18 + w^2*x^16 + 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 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 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 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 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 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1|0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 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 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1|0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 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 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 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 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 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 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 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 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 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 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 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 1 1 0 0 0 0 0 1 0 1 0 0 0 0 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 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 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 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 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 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 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 0 0 1 0 1 0 0 0 1 1 1 0 0 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 1 1 0 0 1 1 1 1 1 0 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0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 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 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 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 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 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 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0|0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 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 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 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 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 0 0 0 0 0 0 0 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 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 1] last modified: 2006-04-03