Bounds on the minimum distance of additive quantum codes

Bounds on [[66,22]]2

lower bound:11
upper bound:16

Construction

Construction of a [[66,22,11]] quantum code:
[1]:  [[64, 23, 11]] quantum code over GF(2^2)
     quantum twisted code of length 64 with interval [ 1, 2, 3, 4, 5, 6, 7, 8, 9 ] and parameter kappa 3
[2]:  [[64, 22, 11]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[66, 22, 11]] 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 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 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 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 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 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 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 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 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 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 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 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 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 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 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 0 0 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 1 0 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 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 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 1 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 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 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 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 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 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 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 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 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 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 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 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 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 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 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 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 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 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 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 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 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 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 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 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 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 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 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 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 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 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 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 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 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 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 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 0 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 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 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 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 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 1 1 1 1 0 1 0 0 1 0 1 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 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 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 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 0 0 1 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 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 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 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 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 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 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 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 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 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 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 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 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 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 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 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 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 0 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 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 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 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 1 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 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 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 1 1 1 0 0 1 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 0 0 0 0 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 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|1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0]
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last modified: 2018-04-03

Notes


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