Bounds on the minimum distance of additive quantum codes

Bounds on [[71,39]]2

lower bound:7
upper bound:10

Construction

Construction type: Gra

Construction of a [[71,39,7]] quantum code:
[1]:  [[71, 39, 7]] quantum code over GF(2^2)
     Construction from a stored generator matrix

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

last modified: 2006-05-31

Notes


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