lower bound: | 9 |
upper bound: | 12 |
Construction of a [[42,10,9]] quantum code: [1]: [[42, 10, 9]] quantum code over GF(2^2) QuasiCyclicCode of length 42 stacked to height 2 with generating polynomials: x^8 + w*x^6 + x^5 + w*x^4 + w^2*x^3 + w^2*x^2 + w^2*x + w^2, w*x^17 + x^16 + x^15 + x^14 + w*x^13 + x^10 + w^2*x^9 + w*x^8 + w^2*x^7 + w^2*x^6 + x^5 + x^4 + x^3 + w*x^2 + w^2*x + 1, 0, x^18 + w^2*x^16 + x^15 + w*x^14 + w*x^11 + x^9 + w*x^8 + w^2*x^7 + w^2*x^4 + w*x^2 + w^2*x + 1 stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 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 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 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 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0|0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 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 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0|0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 0 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 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1|0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 1] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0|0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 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 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0|0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 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 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 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 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 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 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 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 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 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 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 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 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 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 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 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 0 1 1 0 1 0 0 1 1 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 1 1 0 1 0 0 1 1 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 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 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 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 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 0 1 1 0 1 0 0 1 1 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 1 1 0 1 0 0 1 1 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 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 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 1 1 0 0 1 0 0 1 0 1 0 0 0 0 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 1 1 0 1 0 0 1 1 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 1 1 0 1 0 0 1 1 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 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1] last modified: 2024-05-23