Bounds on the minimum distance of additive quantum codes

Bounds on [[85,61]]2

lower bound:6
upper bound:8

Construction

Construction of a [[85,61,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[84, 61, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 6, 16, 19, 21, 22, 24, 25, 26, 29, 30, 31, 34, 44, 45, 46, 50, 52, 56, 57, 63, 65, 66, 67, 72, 74, 76, 84, 86, 87, 89, 90, 93, 95, 98, 101, 108, 109, 112, 119, 123, 126 }
[3]:  [[85, 61, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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