Bounds on the minimum distance of additive quantum codes

Bounds on [[108,87]]2

lower bound:5
upper bound:6

Construction

Construction of a [[108,87,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[106, 88, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 20, 22, 23, 27, 28, 29, 34, 39, 45, 46, 48, 50, 55, 63, 87, 99 }
[3]:  [[106, 87, 5]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[108, 87, 5]] quantum code over GF(2^2)
     ExtendCode [3] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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