Bounds on the minimum distance of additive quantum codes

Bounds on [[197,180]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[197,180,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[197, 183, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 4, 19, 26, 38, 39, 43, 53, 64, 75, 86, 89, 92, 94, 100, 116, 120, 122, 130, 134, 139, 142, 160, 161, 162, 174, 178, 179, 193, 194, 198, 206, 208, 211, 221, 223, 224, 227, 228, 229, 233, 235, 236, 237, 238, 242, 243, 245, 246, 248, 249, 250, 252 }
[3]:  [[197, 180, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 1 1|1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 0 1 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 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 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 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1|0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1]
      [0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0|0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1|0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1]
      [0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 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 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1|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 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 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 0 1 0 1 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 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 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 0 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 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 0 1 0 1 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 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0|0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 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 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1]
      [0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0|0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0|0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1]
      [0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0|0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0]
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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 [[197,180]]2

Construction

Notes

Bounds on [[197,180]]₂
