Bounds on the minimum distance of additive quantum codes

Bounds on [[145,123]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[145,123,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[145, 131, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 10, 11, 12, 16, 17, 18, 20, 26, 33, 34, 35, 37, 38, 40, 49, 52, 55, 56, 57, 59, 64, 70, 75, 80, 83, 85, 88, 90, 92, 93, 95, 96, 101, 104, 107, 108, 111, 112, 113, 114, 115, 120, 122, 125, 126, 127, 129, 131, 133, 134, 136, 139, 142, 144, 147, 153, 154, 155, 156, 158, 162, 163, 164, 165, 167, 170, 171, 174, 178, 180, 188, 189, 191, 193, 197, 198, 200, 201, 204, 208, 209, 210, 212, 214, 217, 218, 219, 220, 221, 223, 226, 227, 230, 231, 232, 234, 235, 238, 240, 241, 244, 245, 249, 250, 251, 252 }
[3]:  [[145, 123, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

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 [[145,123]]2

Construction

Notes

Bounds on [[145,123]]₂
