Bounds on the minimum distance of additive quantum codes

Bounds on [[96,75]]2

lower bound:5
upper bound:6

Construction

Construction of a [[96,75,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[127, 106, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 128
[3]:  [[96, 75, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 1, 9, 11, 19, 20, 23, 24, 26, 28, 30, 38, 40, 41, 42, 47, 48, 52, 54, 57, 66, 67, 73, 76, 77, 83, 86, 96, 101, 106, 109, 117 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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