Bounds on the minimum distance of additive quantum codes

Bounds on [[88,68]]2

lower bound:5
upper bound:6

Construction

Construction of a [[88,68,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[86, 68, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 49, 62, 69, 70, 72, 73, 74, 76, 77, 79, 80, 81, 83, 90, 91, 92, 93, 94, 97, 98, 99, 100, 101, 103, 107, 108, 109, 110, 111, 112, 113, 115, 116, 118, 119, 121 }
[3]:  [[88, 68, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 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 1 0 0 0 1 0 1 0 1 1 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 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0|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 0 1 0 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 0]
      [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 1 0 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0|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 1 1 0 0 1 1 1 0 0 0 0 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 1 1 1 0 0 0 1 1 1 0 1 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 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 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 0 1 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 0 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 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 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0|1 1 0 1 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 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0]
      [0 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 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0|1 0 1 0 0 1 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 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 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 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 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 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0]
      [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 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 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 0 0 1 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 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 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 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0|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 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 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 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 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0|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 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 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 1 1 0 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0|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 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 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 1 0 0 1 0 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 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 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 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 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 0 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0|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 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 1 0 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 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 1 1 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0|0 0 1 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 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 1 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 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 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 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 1 0 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 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 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 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 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 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 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 1 1 1 0 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 0 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 0 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 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 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 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0|1 0 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 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 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 0 1 0 1 0 0 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 0|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 1 1 0 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]

last modified: 2006-04-03

Notes


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