Bounds on the minimum distance of additive quantum codes

Bounds on [[31,9]]2

lower bound:7
upper bound:8

Construction

Construction type: EzermanLingOzkayaSole

Construction of a [[31,9,7]] quantum code:
[1]:  [[31, 9, 7]] quantum code over GF(2^2)
     ConstructionX using quasicyclic codes [30,11], [30,10], and auxiliary code [1,1]

    stabilizer matrix:

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

last modified: 2020-08-22

Notes


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