Bounds on the minimum distance of additive quantum codes

Bounds on [[150,136]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[150,136,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[150, 136, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 6, 7, 8, 9, 11, 13, 14, 16, 17, 18, 20, 21, 22, 23, 24, 28, 35, 36, 44, 46, 47, 60, 65, 66, 69, 73, 75, 76, 77, 79, 82, 83, 89, 92, 93, 94, 95, 98, 101, 102, 104, 107, 109, 118, 119, 121, 122, 123, 134, 137, 139, 140, 143, 144, 148, 149, 156, 158, 161, 162, 163, 165, 167, 170, 172, 178, 182, 183, 185, 192, 193, 200, 201, 203, 205, 206, 207, 208, 210, 211, 213, 216, 218, 222, 223, 225, 226, 227, 228, 229, 230, 231, 232, 234, 239, 240, 244, 245, 247, 249, 251, 252 }

    stabilizer matrix:

      [1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0|0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1|1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1]
      [0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 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 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 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 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1|0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 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 1 1 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 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1]
      [0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 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 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1|0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1]
      [0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 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 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1|0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1]
      [0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1|0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1|0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 0]
      [0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0|0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1]
      [0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1|0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 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 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 1 0 0 0 0 0 0 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 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 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 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 [[150,136]]2

Construction

Notes

Bounds on [[150,136]]₂
