Bounds on the minimum distance of additive quantum codes

Bounds on [[74,55]]2

lower bound:5
upper bound:6

Construction

Construction of a [[74,55,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[74, 56, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 16, 20, 21, 23, 24, 25, 28, 29, 32, 33, 36, 37, 39, 40, 42, 44, 46, 52, 57, 58, 60, 62, 69, 71, 73, 74, 75, 76, 78, 79, 81, 82, 86, 87, 91, 96, 101, 102, 103, 104, 105, 114, 117, 119, 120, 121 }
[3]:  [[74, 55, 5]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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