Bounds on the minimum distance of additive quantum codes

Bounds on [[44,5]]2

lower bound:10
upper bound:14

Construction

Construction of a [[44,5,10]] quantum code:
[1]:  [[48, 0, 14]] self-dual quantum code over GF(2^2)
     quasicyclic code of length 48 stacked to height 2 with 4 generating polynomials
[2]:  [[43, 5, 10]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 14, 17, 22, 23, 45 }
[3]:  [[44, 5, 10]] 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 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 0 1 1 0|1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 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 0 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 1 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0|0 0 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 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 0 0 0 1 0 0 0 1 0 0|1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 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 1 1 0 0 1 0 0|1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 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 1 1 1 0 0 1 0 0|1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0|1 1 1 0 1 0 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 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 1 1 1 0 0 0 1 0|1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 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 0 0 0 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 0 0 1 0 0|1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 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 1 0 0 0 0 1 1 0|1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 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 1 1 0 0 0 1 0|1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 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 1 1 1 0 0 0 1 0|1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 1 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 1 0 0 0 0 0|1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 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 1 0|0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 1 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 1 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 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 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 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 1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 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 1 0 1 0 0 1 0 0|0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 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 1 1 0 0 0 0 1 0|0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0|0 0 1 0 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0|1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0|1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0|0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0|1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0|1 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0|1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0|1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 1 1 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 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0|0 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 1 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 0 0 0 1 1 0 0 0 1 0|0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0|1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 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 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0|0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 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 1 0 0 0 0 1 0 1 0 0 1 0 0|1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0|0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0|1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 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 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0|0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 0 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 0 0 1 1 0 0 0 0 1 0 0|0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 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 0 0 0 0 0 0 0 1 0 0 1 0|1 0 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 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 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 0|0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 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 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]

last modified: 2006-04-03

Notes


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