Bounds on the minimum distance of additive quantum codes

Bounds on [[84,66]]2

lower bound:5
upper bound:6

Construction

Construction of a [[84,66,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[84, 66, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 69, 72, 74, 75, 76, 77, 78, 79, 80, 83, 84, 85, 87, 89, 92, 95, 96, 97, 98, 99, 101, 103, 104, 107, 108, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 122 }

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