Bounds on the minimum distance of additive quantum codes

Bounds on [[46,6]]2

lower bound:10
upper bound:15

Construction

Construction type: Gra

Construction of a [[46,6,10]] quantum code:
[1]:  [[46, 6, 10]] 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 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0|1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 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 1 1 0 0 1 0|1 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0|0 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0|0 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 0 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 0 0 0 0 0 0 1 1 0 0 1 0|0 0 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1|1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1|1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 0 1 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 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 1 0 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0|1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0|1 1 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0|1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 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 0 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 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0|1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1|0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1]
      [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 1 0 0 0 1 0|0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 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 0 0 0 0 0 0 0 1 0 1 0 1 0|1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 1 1]
      [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 1 0 1 1 1|0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 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 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1|1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 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 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 1 0 1|0 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1|1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 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 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 1 1 0 1 0|0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 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 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 1 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 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 0 0 0 1 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 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 1 0 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0|0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1|1 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0|1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0|1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0|1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1|0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1|1 1 0 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1|1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 1 1 1|1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1|0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 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 0 1 0 0 0 0 0 0 1 1 0 1 0 1|0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1|0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0|0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 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 0 0 0 0 1 0 0 0 1 0 1 0 1 0|0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1|1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1|1 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1|1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0]

last modified: 2006-05-27

Notes


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