Bounds on the minimum distance of additive quantum codes

Bounds on [[157,133]]₂

lower bound:	5
upper bound:	6
Construction

Construction of a [[157,133,5]] quantum code:
[1]:  [[256, 230, 6]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 5
[2]:  [[158, 132, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 6, 9, 11, 13, 15, 23, 24, 28, 29, 33, 34, 39, 42, 44, 45, 48, 51, 53, 56, 57, 62, 63, 66, 71, 79, 81, 86, 87, 88, 95, 96, 99, 103, 104, 105, 106, 108, 110, 112, 114, 116, 118, 120, 122, 125, 127, 129, 135, 138, 139, 140, 141, 144, 145, 149, 150, 151, 152, 154, 156, 157, 160, 161, 162, 164, 166, 169, 170, 174, 176, 177, 178, 180, 182, 185, 186, 188, 191, 193, 197, 199, 213, 216, 219, 220, 221, 223, 226, 228, 233, 235, 236, 242, 243, 247, 249, 254 }
[3]:  [[157, 133, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at { 158 }

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0|1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1|0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1]
      [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0|0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0|0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 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 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 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 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 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 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1|0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1|0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
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      [0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 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 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1|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 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 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 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 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 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 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 [[157,133]]2

Construction

Notes

Bounds on [[157,133]]₂
