Bounds on the minimum distance of additive quantum codes

Bounds on [[77,37]]₂

lower bound:	9
upper bound:	14
Construction

Construction of a [[77,37,9]] quantum code:
[1]:  [74, 19] Linear Code over GF(2^2)
     QuasiTwistedCyclicCode of length 74 and constant w^2 stacked to heigth 2 with generators: x^19 + x^18 + w^2*x^17 + x^15 + x^13 + w*x^12 + w^2*x^11 + w*x^10 + x^9 + w^2*x^8 + w^2*x^7 + w^2*x^6 + w*x^4 + w^2*x^2 + w*x + w^2,  w*x^35 + w^2*x^34 + w^2*x^32 + x^31 + w^2*x^29 + w^2*x^27 + x^26 + w^2*x^24 + w^2*x^23 + w*x^22 + w*x^21 + w*x^20 + w^2*x^19 + w^2*x^18 + w*x^17 + w*x^16 + w^2*x^14 + x^10 + w*x^8 + x^6 + w^2*x^4 + w*x^3 + w*x^2 + w^2*x + 1,  0,  x^36 + w^2*x^35 + w*x^34 + x^33 + w^2*x^32 + w*x^31 + x^30 + w^2*x^29 + w*x^28 + x^27 + w^2*x^26 + w*x^25 + x^24 + w^2*x^23 + w*x^22 + x^21 + w^2*x^20 + w*x^19 + x^18 + w^2*x^17 + w*x^16 + x^15 + w^2*x^14 + w*x^13 + x^12 + w^2*x^11 + w*x^10 + x^9 + w^2*x^8 + w*x^7 + x^6 + w^2*x^5 + w*x^4 + x^3 + w^2*x^2 + w*x + 1
[2]:  [[75, 37, 9]] quantum code over GF(2^2)
     QuantumConstructionX applied to [1] with e = 1
[3]:  [[77, 37, 9]] quantum code over GF(2^2)
     ExtendCode [2] by 2

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

last modified: 2024-06-07
Notes

All codes establishing the lower bounds where constructed using MAGMA.
Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
For n>100, the upper bounds on qubit codes are weak (and not necessarily monotone in k).
Some additional information can be found in the book by Nebe, Rains, and Sloane.
My apologies to all authors that have contributed codes to this table for not giving specific credits.
This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024
Bounds on the minimum distance of additive quantum codes

Bounds on [[77,37]]2

Construction

Notes

Bounds on [[77,37]]₂
