Bounds on the minimum distance of additive quantum codes

Bounds on [[132,115]]₂

lower bound:	4
upper bound:	5
Construction

Construction of a [[132,115,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[132, 118, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 18, 22, 24, 25, 27, 31, 37, 39, 40, 43, 46, 48, 50, 52, 54, 56, 61, 68, 71, 78, 80, 84, 87, 88, 92, 93, 94, 102, 103, 104, 106, 109, 112, 117, 120, 121, 122, 123, 127, 128, 130, 134, 135, 137, 139, 140, 146, 147, 151, 152, 153, 156, 157, 158, 159, 160, 161, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 177, 178, 179, 180, 184, 185, 186, 188, 190, 191, 194, 196, 197, 198, 201, 203, 204, 205, 206, 207, 208, 209, 212, 213, 214, 217, 218, 223, 225, 231, 232, 235, 238, 241, 242, 243, 244, 246, 247, 249, 251, 252 }
[3]:  [[132, 115, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1|1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1]
      [0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1|0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 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 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0|0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1|0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0|0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 1]
      [0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1|0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1|0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0]
      [0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1|0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0|0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0]
      [0 0 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
      [0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 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 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 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 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 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 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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|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 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 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 [[132,115]]2

Construction

Notes

Bounds on [[132,115]]₂
