Bounds on the minimum distance of additive quantum codes

Bounds on [[155,140]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[155,140,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[155, 141, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 9, 11, 15, 24, 26, 27, 30, 31, 32, 37, 40, 41, 52, 53, 58, 60, 62, 64, 69, 71, 73, 74, 76, 77, 78, 80, 83, 88, 92, 96, 101, 105, 109, 111, 112, 114, 115, 116, 120, 123, 124, 127, 130, 131, 133, 134, 135, 138, 141, 142, 143, 144, 147, 153, 157, 163, 167, 170, 171, 174, 177, 182, 185, 186, 190, 197, 201, 202, 203, 206, 207, 208, 209, 221, 222, 224, 225, 226, 227, 228, 229, 230, 232, 236, 237, 238, 240, 241, 243, 244, 245, 246, 247, 248, 250, 251 }
[3]:  [[155, 140, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [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 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 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 0 0 1 0 0 0 1 0 1 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 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 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 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 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 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 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 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 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 1 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1|1 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 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 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1|0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0]
      [0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0|0 1 0 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0]
      [0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1|0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0]
      [0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0|0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1]
      [0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1]
      [0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1|0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0]
      [0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 0|0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0]
      [0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0|0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1]
      [0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 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 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0|0 0 0 0 0 1 0 1 0 0 1 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 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 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 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 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 1 1 1 1 1 1 1 0 1 1 0 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 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 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 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 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 1 1 1 1 1 1 1 0 1 1 0 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 [[155,140]]2

Construction

Notes

Bounds on [[155,140]]₂
