Bounds on the minimum distance of additive quantum codes

Bounds on [[127,79]]₂

lower bound:	9
upper bound:	15
Construction

Construction of a [[127,79,9]] quantum code:
[1]:  [[255, 207, 9]] quantum code over GF(2^2)
     BCH code with parameters 255 9
[2]:  [[127, 79, 9]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 5, 6, 7, 8, 13, 15, 19, 20, 21, 24, 25, 29, 31, 32, 33, 37, 40, 42, 45, 49, 50, 51, 54, 58, 60, 61, 62, 63, 66, 69, 70, 72, 73, 74, 77, 79, 81, 85, 86, 87, 90, 91, 94, 95, 96, 97, 100, 101, 102, 104, 105, 108, 111, 112, 113, 114, 118, 121, 122, 124, 125, 126, 127, 130, 132, 133, 134, 140, 143, 145, 147, 148, 149, 152, 154, 156, 159, 160, 161, 162, 164, 168, 171, 172, 174, 175, 177, 183, 184, 185, 187, 189, 190, 196, 198, 199, 202, 203, 204, 206, 207, 209, 210, 211, 213, 214, 215, 220, 221, 222, 223, 225, 227, 229, 230, 233, 234, 235, 236, 238, 239, 244, 247, 250, 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 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 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 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 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 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 0 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 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 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 1 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 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 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 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 0 0 0 1 1 1 1 0 0 1 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 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 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 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 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 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 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 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 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 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 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 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 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 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 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 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 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 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 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 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 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 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 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 0 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 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 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 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 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 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 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 0 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 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 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 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 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 1 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 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 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 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 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 1 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 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 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 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 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 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 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 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 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 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 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 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 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 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 1 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 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 1 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 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 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 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 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 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 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 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 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 0 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 1 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 0 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 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 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|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 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 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 0|0 1 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 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 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 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 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 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 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 1 1 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 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 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 [[127,79]]2

Construction

Notes

Bounds on [[127,79]]₂
