Bounds on the minimum distance of additive quantum codes

Bounds on [[94,69]]2

lower bound:6
upper bound:8

Construction

Construction of a [[94,69,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[92, 69, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 7, 58, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 72, 76, 78, 79, 82, 83, 84, 85, 88, 90, 93, 95, 97, 104, 110, 112, 113, 114, 117, 119, 123, 124, 125, 128 }
[3]:  [[94, 69, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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