Bounds on the minimum distance of additive quantum codes

Bounds on [[108,91]]2

lower bound:4
upper bound:5

Construction

Construction of a [[108,91,4]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[108, 90, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 13, 14, 20, 31, 36, 43, 44, 45, 48, 54, 56, 92, 94, 98 }
[3]:  [[107, 91, 4]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at 108
[4]:  [[108, 91, 4]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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