Bounds on the minimum distance of additive quantum codes

Bounds on [[33,9]]2

lower bound:7
upper bound:9

Construction

Construction of a [[33,9,7]] quantum code:
[1]:  [[32, 10, 7]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[32, 9, 7]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[33, 9, 7]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


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