Bounds on the minimum distance of additive quantum codes

Bounds on [[50,3]]2

lower bound:12
upper bound:17

Construction

Construction of a [[50,3,12]] quantum code:
[1]:  [[54, 0, 16]] self-dual quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[50, 4, 12]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 51, 52, 53, 54 }
[3]:  [[50, 3, 12]] quantum code over GF(2^2)
     Subcode of [2]

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

last modified: 2006-04-03

Notes


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