Bounds on the minimum distance of additive quantum codes

Bounds on [[138,121]]₂

lower bound:	4
upper bound:	5
Construction

Construction of a [[138,121,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[138, 124, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 5, 6, 9, 10, 12, 13, 17, 18, 21, 22, 23, 24, 28, 31, 37, 39, 40, 41, 42, 44, 45, 48, 50, 51, 52, 54, 57, 58, 60, 62, 63, 64, 65, 66, 67, 70, 72, 79, 81, 82, 83, 85, 91, 93, 94, 95, 99, 100, 102, 104, 108, 109, 111, 112, 113, 115, 116, 118, 119, 120, 121, 123, 127, 129, 135, 137, 138, 142, 150, 158, 161, 163, 166, 167, 172, 173, 174, 176, 177, 178, 179, 182, 183, 184, 185, 191, 192, 194, 200, 201, 202, 204, 207, 210, 217, 218, 225, 229, 230, 231, 233, 234, 235, 237, 238, 239, 241, 242, 244, 245, 247, 248, 249, 251 }
[3]:  [[138, 121, 4]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

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 [[138,121]]2

Construction

Notes

Bounds on [[138,121]]₂
