Bounds on the minimum distance of additive quantum codes

Bounds on [[89,79]]2

lower bound:3
upper bound:3

Construction

Construction of a [[89,79,3]] quantum code:
[1]:  [[99, 89, 3]] quantum code over GF(2^2)
     quasicyclic code of length 99 with 8 generating polynomials
[2]:  [[89, 79, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 22, 55, 66, 77, 83, 84, 85, 87, 94, 97 }

    stabilizer matrix:

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