Bounds on the minimum distance of additive quantum codes

Bounds on [[136,109]]₂

lower bound:	6
upper bound:	8
Construction

Construction of a [[136,109,6]] quantum code:
[1]:  [[256, 230, 6]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 5
[2]:  [[136, 110, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 8, 9, 10, 13, 15, 17, 18, 22, 23, 25, 30, 35, 36, 39, 40, 43, 47, 51, 52, 54, 55, 56, 57, 58, 60, 63, 66, 71, 73, 76, 77, 78, 79, 82, 83, 84, 85, 89, 90, 92, 93, 94, 96, 105, 106, 110, 111, 116, 118, 119, 121, 125, 126, 127, 131, 133, 134, 135, 139, 140, 142, 144, 145, 148, 149, 150, 152, 155, 156, 157, 160, 162, 163, 164, 165, 170, 173, 174, 176, 178, 182, 184, 186, 188, 190, 194, 195, 197, 199, 203, 204, 206, 208, 209, 212, 213, 214, 215, 216, 217, 218, 219, 222, 223, 225, 227, 228, 229, 230, 231, 234, 236, 238, 244, 248, 249, 250, 251, 253, 255 }
[3]:  [[136, 109, 6]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2009-02-08
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 [[136,109]]2

Construction

Notes

Bounds on [[136,109]]₂
