Bounds on the minimum distance of additive quantum codes

Bounds on [[53,7]]2

lower bound:11
upper bound:17

Construction

Construction of a [[53,7,11]] quantum code:
[1]:  [[62, 0, 18]] self-dual Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[53, 9, 11]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 7, 13, 22, 24, 26, 31, 32, 42, 60 }
[3]:  [[53, 7, 11]] 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 1 0 1 0 1 1|0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1|1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 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 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 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 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 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 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 0 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 1 0 1 1 0 0|1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 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 0 1 0 0 1 0 0 0|1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0|1 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 1 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 0 0 0 0 0 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|1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 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 1 1 0 0 0 1 0|1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1|1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 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 1 1 0 0 1 1 0|1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 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 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 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 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 1 0 1 1 0 1|1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 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 1 0 0 0 0 0 1|1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 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|0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 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 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 0 1 1 0|1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 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 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 0 1 1|0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 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 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 0 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 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 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|1 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 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 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 1 0 1 0 1|0 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 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 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 1|0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 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 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 1 0 1 0 0|1 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1 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 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 1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 1 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 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|0 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 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 0 1 0 1 0|1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 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 1 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|1 1 1 0 0 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 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 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 1 1|0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1|0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 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 0 0 0 0 0 1 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 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 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 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 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0|0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1|1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 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 1 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 0 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1|0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1|0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0|1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 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 0 1 1 1 1 0 1|0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 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 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 0 1|1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0|0 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 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 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|1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 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 1 0 0 0 0 0 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0 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 1 0 0 0 0 0 0 1 0 0 0 1|0 0 0 0 1 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 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 0 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 0|1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 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 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 0 0 1|1 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 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 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 1|1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 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 0 0 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 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0]

last modified: 2006-04-03

Notes


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