Bounds on the minimum distance of additive quantum codes

Bounds on [[253,239]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[253,239,4]] quantum code:
[1]:  [[286, 272, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[253, 239, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 45, 59, 73, 128, 160, 188, 191, 192, 203, 213, 231, 232, 235, 238, 240, 248, 251, 253, 254, 256, 258, 260, 263, 265, 267, 268, 270, 271, 273, 275, 276, 280, 286 }

    stabilizer matrix:

      [1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0|0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 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 1 0 0 1]
      [0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 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 1 0 0 1|1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1]
      [0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1|0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 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 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1]
      [0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1|0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1]
      [0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1|0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 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 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 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 1 1 1 1 1 1 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 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 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 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 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 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 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 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 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 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 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 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 1|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 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 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 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 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 1 1 1 1 1 1 1 0 0 1 1 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 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 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 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 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 1 1 1 1 1 1 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 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 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 1 1 1 1 1 1 1 0 0 1 1 0 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 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 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 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 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 1 1 1 1 1 1 1 0 0 1 1 0 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 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 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 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 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 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 1 1 1 0 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 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 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 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 1 1 1 1 1 0 0 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 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 1 0 0 0 0 0 0 0 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 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 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 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 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 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 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 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 1 1 1 1 1 1 0 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 [[253,239]]2

Construction

Notes

Bounds on [[253,239]]₂
