lower bound: | 7 |
upper bound: | 9 |
Construction of a [[51,26,7]] quantum code: [1]: [[51, 26, 7]] quantum code over GF(2^2) cyclic code of length 51 with generating polynomial w^2*x^47 + w*x^43 + w*x^41 + x^40 + x^38 + w^2*x^37 + x^36 + w^2*x^35 + w*x^34 + w^2*x^33 + w*x^32 + w^2*x^30 + x^29 + w^2*x^28 + x^27 + w*x^24 + w*x^23 + w*x^22 + w^2*x^21 + x^20 + w^2*x^19 + x^18 + w^2*x^17 + w^2*x^16 + w*x^15 + w*x^14 + x^13 + w*x^12 + w stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0|1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0|0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0|0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 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 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0|0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1|0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0|0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0|0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1|0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 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 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 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 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 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 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1] last modified: 2022-08-02