Bounds on the minimum distance of additive quantum codes

Bounds on [[45,19]]2

lower bound:7
upper bound:10

Construction

Construction of a [[45,19,7]] quantum code:
[1]:  [[42, 20, 7]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[42, 19, 7]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[45, 19, 7]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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

last modified: 2024-05-23

Notes


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