Bounds on the minimum distance of additive quantum codes

Bounds on [[135,120]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[135,120,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[135, 121, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 9, 10, 12, 15, 17, 18, 19, 28, 32, 34, 39, 41, 43, 44, 45, 48, 49, 50, 52, 54, 58, 59, 60, 61, 63, 67, 68, 70, 72, 73, 75, 76, 77, 79, 80, 81, 85, 86, 89, 90, 91, 92, 93, 94, 96, 98, 101, 102, 103, 107, 108, 109, 110, 114, 116, 117, 118, 120, 121, 122, 125, 126, 128, 129, 131, 132, 137, 138, 139, 142, 144, 147, 149, 151, 153, 155, 157, 164, 165, 170, 171, 172, 173, 174, 175, 176, 181, 183, 184, 186, 187, 188, 189, 191, 192, 199, 203, 209, 210, 211, 212, 216, 217, 220, 221, 224, 225, 228, 230, 238, 240, 242, 245, 247, 252 }
[3]:  [[135, 120, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 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 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 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 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1|1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0]
      [0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 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 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0|0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0]
      [0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0|0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1]
      [0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 1|0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0]
      [0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1|0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0|0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0]
      [0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 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 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1|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 0 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1]
      [0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1|0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 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 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 1 1 0 1 1]
      [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 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 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 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 1 1 1 1 1 1 1 1 0 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 [[135,120]]2

Construction

Notes

Bounds on [[135,120]]₂
