Bounds on the minimum distance of additive quantum codes

Bounds on [[89,78]]2

lower bound:3
upper bound:4

Construction

Construction of a [[89,78,3]] quantum code:
[1]:  [[93, 83, 3]] quantum code over GF(2^2)
     quasicyclic code of length 93 stacked to height 2 with 6 generating polynomials
[2]:  [[88, 78, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 10, 28, 29, 61, 79 }
[3]:  [[89, 78, 3]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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