lower bound: | 8 |
upper bound: | 10 |
Construction of a [[44,16,8]] quantum code: [1]: [42, 14] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 42 stacked to height 2 with generating polynomials: x^8 + w^2*x^6 + x^5 + x^4 + x^3 + w^2*x^2 + w*x + 1, w^2*x^18 + w^2*x^17 + w^2*x^16 + w^2*x^12 + w*x^11 + w*x^10 + x^8 + w*x^7 + w^2*x^6 + x^5 + x^4 + w*x^3 + w^2*x^2 + w^2, 0, x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 [2]: [[44, 16, 8]] quantum code over GF(2^2) QuantumConstructionX applied to [1] with e = 2 stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 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 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0|1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 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 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0|0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1] [0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1|0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1] [0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1|0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 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 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 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 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0|0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1] [0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 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 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 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 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1] [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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0] last modified: 2024-06-15