Bounds on the minimum distance of additive quantum codes

Bounds on [[90,71]]2

lower bound:5
upper bound:6

Construction

Construction of a [[90,71,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[90, 72, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 72, 73, 75, 76, 78, 80, 83, 85, 86, 87, 88, 92, 93, 96, 97, 98, 99, 100, 101, 103, 106, 108, 109, 110, 111, 112, 115, 116, 118, 119, 121 }
[3]:  [[90, 71, 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 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1|0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 1 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 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1|0 0 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 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 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0|0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 1 0 0 0 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1|0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 1 0 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 0 1 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 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 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 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1|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 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1|1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 0 1]
      [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 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 1 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 0 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 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 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1|0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 1 1 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 0 0 1 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1|0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1]
      [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 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 1 0 0 0 0 0 1]
      [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 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1|1 0 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 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 1 1 0 1 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 1 1]
      [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 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1|1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 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 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 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 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 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 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1|0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 0 1 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 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0|1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 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 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0|1 0 1 0 1 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 1 0 0 1 0 1 0 0 0 0 1 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 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 1|1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 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 1 0 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1|1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 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 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 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 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 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0]

last modified: 2006-04-03

Notes


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