Bounds on the minimum distance of additive quantum codes

Bounds on [[54,32]]2

lower bound:6
upper bound:8

Construction

Construction type: DastbastehLisonek

Construction of a [[54,32,6]] quantum code:
[1]:  [[54, 32, 6]] quantum code over GF(2^2)
     applying Construction X to a cyclic code [51,40,6]_4
Construction from a stored generator matrix

    stabilizer matrix:

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

last modified: 2022-11-10

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024