Bounds on the minimum distance of additive quantum codes

Bounds on [[68,46]]2

lower bound:5
upper bound:7

Construction

Construction of a [[68,46,5]] quantum code:
[1]:  [[69, 45, 6]] quantum code over GF(2^2)
     quasicyclic code of length 69 stacked to height 2 with 6 generating polynomials
[2]:  [[68, 46, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 69

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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