Bounds on the minimum distance of additive quantum codes

Bounds on [[97,75]]2

lower bound:5
upper bound:6

Construction

Construction of a [[97,75,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[98, 75, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 9, 58, 61, 62, 63, 64, 67, 72, 74, 80, 81, 83, 84, 86, 88, 98, 102, 105, 108, 109, 111, 114, 115, 118, 120, 121, 124, 125, 127 }
[3]:  [[97, 75, 5]] quantum code over GF(2^2)
     Puncturing of [2] at { 98 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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