Bounds on the minimum distance of additive quantum codes

Bounds on [[109,95]]2

lower bound:4
upper bound:4

Construction

Construction of a [[109,95,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[108, 96, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 10, 29, 36, 47, 61, 80, 82, 96, 99, 101, 104, 106, 112, 113, 119, 121, 122 }
[3]:  [[108, 95, 4]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[109, 95, 4]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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