Bounds on the minimum distance of additive quantum codes

Bounds on [[51,3]]2

lower bound:13
upper bound:17

Construction

Construction of a [[51,3,13]] quantum code:
[1]:  [[54, 0, 16]] self-dual quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[51, 3, 13]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 52, 53, 54 }

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

last modified: 2006-04-07

Notes


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