Bounds on the minimum distance of additive quantum codes

Bounds on [[21,0]]2

lower bound:8
upper bound:8

Construction

Construction of a [[21,0,8]] quantum code:
[1]:  [[21, 0, 8]] self-dual 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 1 0 1 1|0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1]
      [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 0 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1]
      [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 1 1 0 0 0 0 1 0 1 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 1 0 0 0|0 0 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0|0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 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 1 0|0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 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 1|0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 0 1]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1|0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0|0 0 0 0 0 1 0 0 0 1 0 1 1 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 1 1 1|0 0 0 0 1 1 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 1 0 0 0 0 0 0 1 0 0 0|0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1]
      [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 1 1 1 1 1 1 1 1 1 0 0 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 1 1 1 1 1 1 1 1 1 0 0 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 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1|0 0 0 0 0 0 0 0 1 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 1 0 1 1 1 0|0 0 0 0 0 1 1 1 0 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 1 0 1 1 1|0 0 0 0 1 1 1 0 1 0 0 1 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|1 0 0 0 1 1 0 1 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 0 0 0|0 1 0 0 0 1 1 0 1 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 0 0|0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0|0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1]

last modified: 2005-06-27

Notes


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