Bounds on the minimum distance of additive quantum codes

Bounds on [[63,27]]2

lower bound:9
upper bound:13

Construction

Construction type: BE

Construction of a [[63,27,9]] quantum code:
[1]:  [[63, 27, 9]] Quantum code over GF(2^2)
     quantum twisted code of length 63 with interval [ 1, 2, 3, 4, 5, 6, 7, 8 ] and parameter kappa 3

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014