Bounds on the minimum distance of additive quantum codes

Bounds on [[92,71]]2

lower bound:5
upper bound:6

Construction

Construction of a [[92,71,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[127, 106, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 128
[3]:  [[92, 71, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 8, 10, 15, 16, 17, 18, 19, 20, 26, 27, 29, 35, 38, 39, 46, 47, 58, 64, 65, 69, 76, 77, 82, 84, 85, 88, 96, 98, 103, 108, 116, 117, 118, 123, 124 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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