Bounds on the minimum distance of additive quantum codes

Bounds on [[78,44]]2

lower bound:7
upper bound:11

Construction

Construction of a [[78,44,7]] quantum code:
[1]:  [[256, 222, 7]] quantum code over GF(2^2)
     Extended BCH code with parameters 255 6
[2]:  [[78, 44, 7]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 129, 130, 131, 132, 134, 136, 137, 141, 142, 143, 146, 150, 156, 159, 160, 162, 163, 165, 166, 170, 175, 177, 178, 179, 180, 182, 183, 186, 187, 188, 191, 192, 194, 197, 198, 204, 206, 207, 208, 209, 210, 214, 216, 217, 220, 224, 226, 227, 229, 233, 234, 238, 240, 243, 247, 249, 251, 253 }

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

last modified: 2009-01-27

Notes


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