Bounds on the minimum distance of additive quantum codes

Bounds on [[151,127]]₂

lower bound:	5
upper bound:	7
Construction

Construction of a [[151,127,5]] quantum code:
[1]:  [[256, 230, 6]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 5
[2]:  [[152, 126, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 13, 16, 18, 21, 22, 25, 26, 27, 29, 31, 40, 43, 44, 45, 46, 48, 51, 60, 61, 63, 64, 66, 72, 73, 75, 78, 79, 80, 81, 82, 84, 85, 86, 88, 89, 90, 92, 94, 98, 99, 100, 102, 105, 106, 108, 109, 110, 111, 113, 115, 116, 127, 128, 129, 130, 131, 135, 137, 138, 142, 143, 148, 152, 153, 155, 156, 157, 159, 164, 165, 170, 171, 173, 177, 180, 187, 192, 193, 194, 200, 201, 208, 211, 213, 215, 217, 218, 220, 221, 225, 226, 227, 228, 232, 234, 237, 239, 243, 245, 246, 247, 250, 252 }
[3]:  [[151, 127, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at { 152 }

    stabilizer matrix:

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

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 [[151,127]]2

Construction

Notes

Bounds on [[151,127]]₂
