Bounds on the minimum distance of additive quantum codes

Bounds on [[43,15]]2

lower bound:7
upper bound:10

Construction

Construction of a [[43,15,7]] quantum code:
[1]:  [[42, 20, 7]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[42, 15, 7]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[43, 15, 7]] quantum code over GF(2^2)
     ExtendCode [2] by 1

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

last modified: 2006-04-03

Notes


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