Bounds on the minimum distance of additive quantum codes

Bounds on [[69,50]]2

lower bound:5
upper bound:6

Construction

Construction of a [[69,50,5]] quantum code:
[1]:  [[68, 50, 5]] quantum code over GF(2^2)
     quasicyclic code of length 68 stacked to height 2 with 8 generating polynomials
[2]:  [[69, 50, 5]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014