Bounds on the minimum distance of additive quantum codes

Bounds on [[143,128]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[143,128,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[143, 129, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 4, 6, 7, 8, 9, 10, 12, 13, 28, 30, 36, 40, 44, 47, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 69, 70, 71, 72, 75, 76, 77, 79, 81, 82, 84, 85, 86, 87, 88, 89, 90, 104, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 121, 122, 124, 127, 132, 133, 136, 137, 139, 140, 141, 145, 146, 148, 149, 151, 154, 158, 162, 163, 166, 168, 174, 176, 177, 181, 183, 186, 187, 194, 195, 199, 201, 203, 206, 209, 210, 211, 212, 216, 217, 218, 219, 223, 229, 233, 235, 240, 241, 242, 243, 245 }
[3]:  [[143, 128, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1|0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0]
      [0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0|1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1]
      [0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0|0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0|0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0]
      [0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1|0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1|0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0]
      [0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0|0 0 0 1 0 0 0 0 0 1 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 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0]
      [0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1|0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0|0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1]
      [0 0 0 0 0 1 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 1 1 1 1 1 1 1 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 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|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 1 1 1 1 1 1 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 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]
      [0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 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 1 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 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1]
      [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 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1|0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 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 1 1 1 1]
      [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 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 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]

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 [[143,128]]2

Construction

Notes

Bounds on [[143,128]]₂
