Bounds on the minimum distance of additive quantum codes

Bounds on [[154,132]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[154,132,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[154, 140, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 5, 6, 7, 9, 12, 13, 18, 20, 21, 22, 26, 28, 33, 34, 39, 42, 43, 45, 46, 51, 53, 59, 61, 65, 66, 68, 77, 83, 84, 86, 87, 89, 90, 92, 95, 96, 99, 107, 112, 114, 117, 119, 121, 124, 125, 126, 127, 129, 133, 139, 140, 141, 145, 149, 150, 164, 165, 168, 169, 170, 171, 175, 176, 180, 185, 193, 194, 195, 200, 201, 203, 206, 208, 212, 216, 220, 222, 224, 226, 228, 231, 232, 233, 236, 237, 238, 240, 241, 242, 243, 245, 246, 248, 249, 250, 251 }
[3]:  [[154, 132, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1|1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1]
      [0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1|0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 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 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 0|0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1]
      [0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 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 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0|0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0|0 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 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1]
      [0 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 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0|0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1]
      [0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 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 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 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 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 1 1 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 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1]
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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 [[154,132]]2

Construction

Notes

Bounds on [[154,132]]₂
