Bounds on the minimum distance of additive quantum codes

Bounds on [[167,143]]₂

lower bound:	5
upper bound:	6
Construction

Construction of a [[167,143,5]] quantum code:
[1]:  [[256, 230, 6]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 5
[2]:  [[168, 142, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 7, 9, 10, 16, 17, 18, 20, 21, 25, 27, 32, 33, 34, 35, 40, 42, 43, 47, 48, 49, 59, 65, 68, 70, 73, 77, 79, 83, 88, 91, 92, 94, 101, 109, 113, 115, 117, 122, 127, 131, 132, 144, 145, 147, 148, 154, 160, 164, 166, 167, 169, 171, 172, 175, 182, 184, 185, 186, 188, 197, 200, 203, 204, 207, 210, 211, 214, 216, 220, 222, 223, 227, 228, 229, 230, 231, 232, 235, 237, 240, 242, 245, 247, 248, 250, 253, 256 }
[3]:  [[167, 143, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at { 168 }

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 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 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0|1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 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 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1|0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 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 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 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 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1|0 0 1 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 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0|0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 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 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1]
      [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 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1|0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1]
      [0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 1|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 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1]
      [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 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1|0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1]
      [0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0|0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 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 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1|0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 0 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 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 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 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 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 [[167,143]]2

Construction

Notes

Bounds on [[167,143]]₂
