Bounds on the minimum distance of additive quantum codes

Bounds on [[121,81]]₂

lower bound:	8
upper bound:	12
Construction

Construction of a [[121,81,8]] quantum code:
[1]:  [[119, 81, 8]] quantum code over GF(2^2)
     cyclic code of length 119 with generating polynomial x^19 + w*x^18 + x^17 + x^15 + x^14 + w^2*x^13 + w*x^12 + w^2*x^10 + w^2*x^7 + w*x^6 + x^4 + w^2*x^3 + x^2 + 1
[2]:  [[121, 81, 8]] quantum code over GF(2^2)
     ExtendCode [1] by 2

    stabilizer matrix:

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

last modified: 2014-11-05
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 even 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: 23.10.2014
Bounds on the minimum distance of additive quantum codes

Bounds on [[121,81]]2

Construction

Notes

Bounds on [[121,81]]₂
