Bounds on the minimum distance of additive quantum codes

Bounds on [[101,82]]2

lower bound:5
upper bound:6

Construction

Construction of a [[101,82,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[100, 82, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 6, 70, 71, 73, 75, 76, 77, 80, 81, 82, 84, 86, 87, 89, 92, 93, 96, 97, 105, 108, 111, 116 }
[3]:  [[101, 82, 5]] 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 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0|1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 1 1 0|0 0 1 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 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 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0|1 1 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0|1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0|1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0|0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 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 1 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0|1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 0 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 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0|1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0|1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 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 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0|0 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0|1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0|0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 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 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0|1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 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 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0|1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 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 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0|0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 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 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0|1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 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 1 0 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0|0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 1 0 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 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 0|0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0]

last modified: 2006-04-03

Notes


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