Bounds on the minimum distance of additive quantum codes

Bounds on [[22,13]]2

lower bound:3
upper bound:4

Construction

Construction of a [[22,13,3]] quantum code:
[1]:  [[21, 15, 3]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[21, 13, 3]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[22, 13, 3]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2005-06-30

Notes


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