lower bound: | 9 |
upper bound: | 13 |
Construction of a [[49,13,9]] quantum code: [1]: [[49, 13, 9]] quantum code over GF(2^2) QuasiCyclicCode of length 49 stacked to height 4 with generating polynomials: 1, 0, w*x^3 + w^2*x + w, w*x^4 + w*x^2 + w, w*x^6 + w*x^3 + w^2*x^2 + x + 1, x^5 + x^3 + x + w^2, w^2*x^5 + x^4 + x + 1, 0, 1, w*x^3 + w^2*x^2 + x + 1, w^2*x^4 + w*x^3 + w*x + w, w*x^5 + w*x^4 + w^2*x^3 + w*x^2 + w^2*x + 1, w^2*x^6 + w^2*x^4 + w^2*x^3 + w^2*x^2, w*x^6 + x^5 + w*x^4 + w*x^2 + w^2*x, 0, 0, x^4 + x^2 + x + 1, x^5 + x^3 + x^2 + x, x^6 + w*x^5 + w^2*x^3 + w*x^2 + w^2*x + 1, w*x^6 + w*x^5 + w*x^2 + w, w*x^5 + w*x^4 + w*x^3 + w, 0, 0, 0, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, w^2*x^6 + w^2*x^5 + w^2*x^4 + w^2*x^3 + w^2*x^2 + w^2*x + w^2, w*x^6 + w*x^5 + w*x^4 + w*x^3 + w*x^2 + w*x + w, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 stabilizer matrix: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 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 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 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 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 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 0 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1] [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 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 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 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 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0] [0 0 1 0 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 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0|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 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 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 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0|0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0] [0 0 0 1 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 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0|0 0 0 0 0 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 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1] [0 0 0 0 0 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 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1] [0 0 0 0 1 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 0 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1|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 1 1 1 0 0 1 1 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1|0 0 0 0 1 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 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0] [0 0 0 0 0 1 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 0 0 0 0 1 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0] 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