Bounds on the minimum distance of additive quantum codes

Bounds on [[131,116]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[131,116,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[131, 117, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 4, 5, 8, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 26, 31, 33, 37, 49, 50, 52, 58, 63, 64, 65, 67, 73, 74, 76, 77, 81, 82, 83, 84, 86, 88, 89, 90, 93, 95, 97, 98, 101, 102, 106, 108, 112, 114, 116, 117, 122, 123, 124, 125, 129, 131, 136, 137, 140, 141, 142, 144, 145, 146, 148, 152, 154, 155, 156, 161, 164, 165, 167, 168, 170, 171, 174, 177, 179, 180, 181, 183, 185, 186, 187, 190, 193, 195, 196, 197, 200, 204, 205, 206, 207, 208, 209, 212, 214, 217, 219, 221, 222, 224, 226, 227, 228, 229, 230, 231, 233, 237, 239, 240, 241, 242, 246, 248, 251 }
[3]:  [[131, 116, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0|0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1]
      [0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1|1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0]
      [0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0|0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0]
      [0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0|0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0]
      [0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1|0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0|0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0]
      [0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1|0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0|0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 1 1 0 1 0]
      [0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0|0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0]
      [0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0|0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 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 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0]
      [0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1|0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 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 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 1 0 0 0 0 0 0 0 0 0 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 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 0 1 0 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 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 1 0 0 0 0 0 0 0 0 0 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 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 0 1 0 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 [[131,116]]2

Construction

Notes

Bounds on [[131,116]]₂
