Bounds on the minimum distance of additive quantum codes

Bounds on [[21,2]]2

lower bound:6
upper bound:7

Construction

Construction of a [[21,2,6]] quantum code:
[1]:  [[16, 2, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[21, 2, 6]] Quantum code over GF(2^2)
     ExtendCode [1] by 5

    stabilizer matrix:

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

last modified: 2005-06-24

Notes


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