Bounds on the minimum distance of additive quantum codes

Bounds on [[169,155]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[169,155,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[169, 155, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 9, 11, 14, 17, 28, 31, 34, 36, 41, 43, 44, 45, 48, 52, 53, 54, 55, 56, 63, 68, 69, 72, 77, 91, 93, 104, 111, 112, 114, 115, 116, 117, 119, 120, 122, 125, 128, 130, 149, 155, 159, 163, 164, 165, 168, 172, 177, 179, 180, 182, 186, 188, 191, 195, 199, 205, 209, 210, 214, 216, 217, 220, 222, 224, 225, 226, 227, 231, 232, 234, 235, 236, 237, 238, 239, 240, 242, 245, 246, 247, 248, 251, 252 }

    stabilizer matrix:

      [1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 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 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 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 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1|1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 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 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0]
      [0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 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 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 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 0 1 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 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 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 0 0 1 1 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 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 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 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 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 0 0 1 1 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 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1|0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 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 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 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 1 1 1 1]
      [0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1|0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1]
      [0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1|0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0]
      [0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1|0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1]
      [0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1|0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0]
      [0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0|0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0]
      [0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0|0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0]
      [0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0|0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0]
      [0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0|0 0 0 0 0 1 0 1 1 1 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 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 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 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 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 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 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 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 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 0 1 1 1 1 1 1 1 1 1 0 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 [[169,155]]2

Construction

Notes

Bounds on [[169,155]]₂
