Bounds on the minimum distance of additive quantum codes

Bounds on [[82,63]]2

lower bound:5
upper bound:6

Construction

Construction of a [[82,63,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[82, 64, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 35, 38, 62, 69, 70, 71, 72, 73, 75, 76, 78, 79, 81, 83, 85, 87, 89, 90, 91, 92, 93, 95, 96, 99, 104, 105, 106, 107, 108, 109, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122 }
[3]:  [[82, 63, 5]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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