Bounds on the minimum distance of additive quantum codes

Bounds on [[75,32]]2

lower bound:9
upper bound:15

Construction

Construction of a [[75,32,9]] quantum code:
[1]:  [[74, 32, 9]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[75, 32, 9]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0|1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 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 1 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0|1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 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 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 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0|1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0|0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0|0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 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 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0|0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 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 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 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0|1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 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 0 0 0 0 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 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0|0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 1 0|0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 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 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 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0|1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0|1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0|0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0|0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 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 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 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 0 0|1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 0 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 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 1 0 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0|1 1 0 1 0 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 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 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 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0|0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 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 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 1 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0|1 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 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 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0|0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 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 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 1 1 0 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0|1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 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 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 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0|0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 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 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 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 0 0 0|1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 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 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0|1 1 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0|0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0|1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 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 0 0 0 0 0 1 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 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 0|0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 0 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 1 0 0 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 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0|0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0|0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 1 0|0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 1 1 0|0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0|1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 0|0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 0]
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last modified: 2006-05-22

Notes


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