Bounds on the minimum distance of additive quantum codes

Bounds on [[19,5]]2

lower bound:5
upper bound:6

Construction

Construction of a [[19,5,5]] quantum code:
[1]:  [[18, 6, 5]] Quantum code over GF(2^2)
     quasicyclic code of length 18 stacked to height 2 with 6 generating polynomials
[2]:  [[18, 5, 5]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[19, 5, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2005-06-27

Notes


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