Bounds on the minimum distance of additive quantum codes

Bounds on [[49,9]]2

lower bound:10
upper bound:15

Construction

Construction type: EzermanGrasslLingOzbudakOzkaya

Construction of a [[49,9,10]] quantum code:
[1]:  [[49, 9, 10]] 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 + 1,  w*x^3 + w^2*x^2 + w*x + w,  w*x^6 + x^4 + w*x^3 + w*x^2 + x + w,  x^6 + x^4 + w*x^3 + w*x^2 + w*x + 1,  x^4 + w*x^2 + w^2*x + w,  0,  1,  w*x^3 + w*x^2 + 1,  w*x^3 + 1,  x^6 + w*x^5 + w^2*x^4 + w*x + w^2,  w^2*x^6 + w*x^5 + w*x^4 + w^2*x^3 + x^2 + w*x,  x^6 + w*x^5 + x^4 + w*x^3 + w^2,  0,  0,  x^4 + x^3 + x^2 + 1,  0,  w*x^6 + w^2*x^5 + w^2*x^4 + x^3 + w*x^2 + x,  w^2*x^6 + x^5 + w^2*x^4 + x^2 + w*x + w,  x^6 + x^5 + x^3 + 1,  0,  0,  0,  x^4 + x^3 + x^2 + 1,  x^6 + x^5 + w*x^4 + w^2*x^3 + w*x^2 + w^2,  w*x^6 + w^2*x^5 + x^4 + w^2*x^3 + x + w,  w*x^5 + x^4 + x^3 + w^2*x^2 + w*x + w^2

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 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 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 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 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 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 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 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 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 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 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0|0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 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 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1|0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 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 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 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 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0|0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 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 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 1|0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1]
      [0 0 0 0 0 1 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 0 1 1 0 1 0 1 1 1 0 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 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 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 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0]
      [0 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 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 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 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 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 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 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 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 1 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 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 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 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 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 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 1 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 0 1 0 1 0 0 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 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 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 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 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 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 1 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 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 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 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 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 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 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 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 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 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 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 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 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 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 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 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 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 1 0 0 1 0 1 1 1 1 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 1 0 0 1 0 1 1 1 1 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 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 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 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 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 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 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 1 1 0 0 1 0 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 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 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 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 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 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 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 0 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 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 1 1 1 0 1 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 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 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 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 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 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 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1]

last modified: 2024-05-23

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024