Bounds on the minimum distance of additive quantum codes

Bounds on [[144,128]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[144,128,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[144, 130, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 10, 13, 16, 18, 22, 23, 24, 26, 27, 29, 31, 35, 39, 43, 48, 50, 51, 53, 58, 59, 64, 66, 69, 71, 74, 78, 85, 86, 89, 92, 94, 95, 97, 98, 99, 100, 106, 107, 109, 110, 115, 116, 120, 121, 124, 125, 126, 129, 133, 134, 135, 143, 145, 148, 151, 152, 153, 155, 160, 165, 166, 168, 170, 172, 175, 177, 178, 180, 181, 183, 185, 188, 191, 194, 195, 199, 204, 206, 207, 208, 209, 210, 212, 213, 216, 218, 219, 221, 223, 225, 226, 227, 228, 229, 230, 233, 236, 237, 238, 241, 242, 243, 245, 247, 248 }
[3]:  [[144, 128, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1|1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1]
      [0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1|0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0]
      [0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1|0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 1]
      [0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1|0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 1 0]
      [0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1|0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0]
      [0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 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 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 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 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1|0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 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 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0]
      [0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 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 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 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 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1|0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 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 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 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]
      [0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 0 1|0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0|0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 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 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 1 1 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 1 0 1 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 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 1 0 1]
      [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 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 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 1 1 1 1 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 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 1 1 1 1 0 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 1 1 1 1 1 1 1 1 1 1 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 [[144,128]]2

Construction

Notes

Bounds on [[144,128]]₂
