Bounds on the minimum distance of additive quantum codes

Bounds on [[162,148]]₂

lower bound:	4
upper bound:	4
Construction

Construction of a [[162,148,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[162, 148, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 7, 10, 11, 16, 18, 20, 24, 29, 31, 37, 38, 40, 41, 43, 47, 48, 52, 53, 55, 56, 57, 66, 67, 71, 72, 75, 76, 80, 85, 87, 88, 91, 94, 98, 105, 112, 113, 114, 116, 119, 120, 121, 123, 124, 125, 126, 129, 133, 136, 139, 149, 151, 154, 155, 156, 172, 176, 177, 183, 186, 190, 194, 197, 200, 206, 207, 208, 209, 217, 222, 223, 224, 225, 226, 227, 229, 232, 236, 237, 238, 239, 242, 243, 244, 245, 246, 248, 250, 251, 252 }

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 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 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 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 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 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 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0|1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 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 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1]
      [0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 0 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 0 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 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 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 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 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 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1|0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1]
      [0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1|0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0]
      [0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 0|0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1]
      [0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1|0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 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 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1]
      [0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 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 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1|0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0]
      [0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 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 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0]
      [0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0|0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 1 0]
      [0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0|0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0]
      [0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0|0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 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 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 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 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 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 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 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 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 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 [[162,148]]2

Construction

Notes

Bounds on [[162,148]]₂
