Bounds on the minimum distance of additive quantum codes

Bounds on [[54,40]]2

lower bound:4
upper bound:5

Construction

Construction of a [[54,40,4]] quantum code:
[1]:  [[62, 50, 4]] quantum code over GF(2^2)
     quasicyclic code of length 62 stacked to height 2 with 4 generating polynomials
[2]:  [[52, 40, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 8, 9, 27, 28, 30, 47, 55, 59, 61, 62 }
[3]:  [[54, 40, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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