Bounds on the minimum distance of additive quantum codes

Bounds on [[23,6]]2

lower bound:5
upper bound:7

Construction

Construction of a [[23,6,5]] 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]:  [[23, 6, 5]] Quantum code over GF(2^2)
     ExtendCode [1] by 5

    stabilizer matrix:

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