Bounds on the minimum distance of additive quantum codes

Bounds on [[55,25]]2

lower bound:7
upper bound:10

Construction

Construction type: Gra

Construction of a [[55,25,7]] quantum code:
[1]:  [[55, 25, 7]] Quantum code over GF(2^2)
     Construction from a stored generator matrix

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014