Bounds on the minimum distance of additive quantum codes

Bounds on [[92,58]]2

lower bound:7
upper bound:11

Construction

Construction of a [[92,58,7]] quantum code:
[1]:  [[256, 222, 7]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 6
[2]:  [[92, 58, 7]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 7, 9, 11, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 27, 28, 35, 36, 37, 41, 44, 46, 47, 48, 49, 51, 52, 56, 57, 59, 62, 63, 65, 67, 68, 71, 73, 74, 75, 76, 77, 79, 80, 82, 83, 84, 86, 88, 89, 92, 95, 96, 97, 98, 100, 101, 103, 104, 105, 106, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 126, 127, 129, 130, 131, 132, 134, 135, 136, 138, 141, 143, 145, 146, 147, 148, 149, 151, 154, 156, 157, 158, 159, 160, 161, 162, 165, 166, 167, 168, 170, 172, 173, 174, 177, 181, 182, 183, 184, 185, 188, 190, 191, 192, 193, 194, 195, 196, 197, 198, 200, 201, 202, 203, 204, 206, 207, 208, 209, 210, 211, 214, 218, 219, 220, 221, 225, 226, 227, 228, 229, 230, 233, 234, 236, 237, 238, 239, 241, 242, 244, 248, 249, 250, 251, 253, 256 }

    stabilizer matrix:

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

last modified: 2009-01-27

Notes


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