Bounds on the minimum distance of additive quantum codes

Bounds on [[185,165]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[185,165,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[185, 171, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 12, 15, 16, 33, 55, 63, 74, 75, 76, 79, 81, 96, 99, 100, 101, 102, 111, 114, 115, 117, 120, 121, 122, 125, 126, 129, 130, 132, 135, 136, 143, 146, 151, 152, 156, 158, 165, 166, 170, 177, 179, 185, 190, 194, 209, 218, 220, 222, 224, 225, 226, 227, 231, 232, 234, 235, 236, 238, 241, 243, 244, 245, 247, 248, 250, 252 }
[3]:  [[185, 165, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 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 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 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 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 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 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1|1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1]
      [0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 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 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 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 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 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 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 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 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 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 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 0 0 0 1 1 0 1 0 1 1 1|0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 0 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 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 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 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 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 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1|0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1|0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1]
      [0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1]
      [0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0|0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1]
      [0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 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 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 1 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 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 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 0 1 1 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 [[185,165]]2

Construction

Notes

Bounds on [[185,165]]₂
