Bounds on the minimum distance of additive quantum codes

Bounds on [[148,128]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[148,128,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[148, 134, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 10, 11, 12, 13, 14, 19, 21, 23, 26, 27, 28, 30, 32, 34, 36, 37, 39, 42, 46, 47, 48, 53, 55, 66, 68, 69, 70, 75, 77, 78, 81, 83, 85, 87, 88, 89, 92, 93, 94, 95, 96, 98, 99, 103, 104, 110, 111, 113, 117, 118, 119, 120, 123, 125, 126, 134, 135, 136, 139, 143, 145, 149, 152, 155, 156, 159, 160, 172, 175, 177, 179, 181, 187, 191, 193, 194, 196, 197, 200, 202, 205, 206, 207, 209, 215, 216, 217, 219, 221, 222, 223, 226, 230, 233, 236, 237, 238, 239, 242, 247, 249, 250, 251 }
[3]:  [[148, 128, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 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 1 0 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1|1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 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 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0]
      [0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 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 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 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 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 1 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 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1|0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1]
      [0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0|0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0]
      [0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1|0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1|0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 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 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 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 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 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 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0|0 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 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 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 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0]
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      [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 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 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 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 [[148,128]]2

Construction

Notes

Bounds on [[148,128]]₂
