Bounds on the minimum distance of additive quantum codes

Bounds on [[32,16]]2

lower bound:6
upper bound:6

Construction

Construction type: linear

Construction of a [[32,16,6]] quantum code:
[1]:  [[32, 16, 6]] Quantum code over GF(2^2)
     from a linear code obtained via Construction XX applied to quasicyclic codes
Construction from a stored generator matrix

    stabilizer matrix:

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

last modified: 2013-12-13

Notes


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