Bounds on the minimum distance of additive quantum codes

Bounds on [[53,12]]2

lower bound:10
upper bound:15

Construction

Construction of a [[53,12,10]] quantum code:
[1]:  [[53, 17, 10]] Quantum code over GF(2^2)
     ConstructionXX using cyclic codes [51,35], [51,34], [51,34], and auxiliary codes [1,1], [1,1]
[2]:  [[53, 12, 10]] Quantum code over GF(2^2)
     Subcode of [1]

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

last modified: 2013-12-09

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014