Bounds on the minimum distance of additive quantum codes

Bounds on [[82,55]]2

lower bound:6
upper bound:8

Construction

Construction of a [[82,55,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[78, 55, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 4, 5, 7, 8, 15, 16, 18, 19, 21, 22, 23, 34, 35, 36, 37, 40, 43, 48, 49, 51, 53, 58, 60, 66, 71, 73, 74, 75, 78, 82, 83, 86, 87, 90, 92, 95, 97, 99, 102, 103, 104, 109, 111, 115, 116, 119, 121, 124 }
[3]:  [[82, 55, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 4

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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