Bounds on the minimum distance of additive quantum codes

Bounds on [[109,100]]2

lower bound:3
upper bound:3

Construction

Construction of a [[109,100,3]] quantum code:
[1]:  [[168, 159, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[109, 100, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 45, 46, 47, 50, 53, 54, 56, 57, 59, 61, 62, 63, 64, 68, 75, 76, 77, 78, 81, 82, 83, 86, 88, 92, 94, 97, 98, 103, 107, 115, 116, 118, 120, 121, 123, 124, 125, 128, 131, 132, 133, 137, 138, 139, 140, 141, 143, 148, 152, 154, 155, 157, 158, 161, 162, 165, 166, 167 }

    stabilizer matrix:

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

last modified: 2008-08-05

Notes


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