Bounds on the minimum distance of additive quantum codes

Bounds on [[92,78]]2

lower bound:4
upper bound:4

Construction

Construction of a [[92,78,4]] quantum code:
[1]:  [[252, 238, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[92, 78, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 5, 6, 7, 8, 9, 10, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 49, 52, 54, 55, 58, 59, 61, 62, 63, 64, 65, 66, 67, 70, 72, 74, 76, 77, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 97, 98, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 114, 115, 116, 117, 120, 123, 126, 127, 128, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 142, 145, 147, 149, 150, 152, 159, 160, 162, 163, 164, 166, 167, 168, 169, 170, 171, 177, 181, 183, 184, 188, 189, 190, 191, 192, 196, 198, 199, 200, 203, 207, 208, 211, 212, 213, 214, 216, 217, 218, 219, 221, 222, 225, 226, 228, 229, 231, 233, 235, 237, 238, 239, 241, 242, 245, 247, 249, 250, 252 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014