Bounds on the minimum distance of additive quantum codes

Bounds on [[123,75]]₂

lower bound:	9
upper bound:	15
Construction

Construction of a [[123,75,9]] quantum code:
[1]:  [[255, 207, 9]] quantum code over GF(2^2)
     BCH code with parameters 255 9
[2]:  [[123, 75, 9]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 24, 25, 26, 29, 31, 32, 33, 39, 40, 42, 43, 45, 49, 51, 55, 56, 60, 62, 63, 65, 67, 70, 71, 72, 75, 77, 78, 80, 82, 84, 86, 88, 91, 93, 97, 98, 100, 102, 103, 104, 106, 110, 115, 116, 118, 119, 123, 131, 132, 135, 138, 140, 141, 143, 145, 148, 149, 153, 154, 155, 156, 157, 158, 163, 164, 165, 167, 169, 172, 174, 175, 177, 178, 180, 181, 184, 185, 186, 188, 189, 190, 191, 192, 195, 196, 200, 201, 204, 205, 206, 210, 212, 214, 215, 218, 220, 221, 222, 226, 227, 229, 231, 232, 233, 234, 236, 237, 241, 246, 247, 249, 250, 251, 252, 254, 255 }

    stabilizer matrix:

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

last modified: 2006-04-03
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 even 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: 23.10.2014
Bounds on the minimum distance of additive quantum codes

Bounds on [[123,75]]2

Construction

Notes

Bounds on [[123,75]]₂
