Bounds on the minimum distance of additive quantum codes

Bounds on [[153,130]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[153,130,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[153, 139, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 4, 6, 7, 9, 16, 21, 22, 24, 28, 30, 31, 34, 36, 42, 43, 44, 46, 48, 52, 53, 56, 58, 59, 63, 66, 68, 69, 71, 79, 87, 92, 99, 101, 102, 104, 105, 108, 109, 112, 114, 115, 117, 118, 119, 121, 123, 125, 128, 130, 132, 134, 136, 142, 153, 154, 158, 167, 168, 171, 174, 175, 177, 183, 184, 185, 186, 187, 188, 195, 197, 198, 203, 206, 212, 213, 214, 215, 216, 220, 222, 224, 225, 226, 227, 228, 229, 231, 232, 235, 236, 237, 238, 240, 244, 246, 247, 250, 251 }
[3]:  [[153, 130, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 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 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0|1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 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 1 1 1 1 0 0 1]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 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 0 1 0 0 0 0 1 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 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 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 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 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1]
      [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1|0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 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 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0|0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1|0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0|0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1]
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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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 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 [[153,130]]2

Construction

Notes

Bounds on [[153,130]]₂
