Bounds on the minimum distance of additive quantum codes

Bounds on [[193,176]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[193,176,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[193, 179, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 5, 8, 18, 20, 21, 28, 45, 50, 64, 65, 70, 78, 79, 89, 92, 93, 96, 102, 109, 112, 116, 119, 120, 122, 125, 126, 147, 148, 151, 155, 156, 172, 175, 176, 178, 185, 192, 194, 206, 209, 214, 216, 217, 220, 221, 229, 231, 232, 234, 237, 238, 241, 242, 244, 245, 248, 249, 251, 252 }
[3]:  [[193, 176, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1|0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 1]
      [0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0|1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0]
      [0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 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 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 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 0 0 1 0 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 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 1 1 1 0 0 1 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 1 1 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 0 0 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 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 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 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 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 1 1 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 0 0 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 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1|0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 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 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 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 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1]
      [0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 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 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1|0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0]
      [0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 1|0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 0 0]
      [0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 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 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0|0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0]
      [0 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 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1|0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 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 [[193,176]]2

Construction

Notes

Bounds on [[193,176]]₂
