Bounds on the minimum distance of additive quantum codes

Bounds on [[79,59]]2

lower bound:5
upper bound:6

Construction

Construction of a [[79,59,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[78, 60, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 9, 10, 11, 16, 17, 18, 19, 23, 27, 34, 36, 38, 39, 43, 44, 45, 46, 48, 50, 52, 57, 63, 64, 68, 78, 85, 86, 87, 90, 91, 94, 96, 100, 101, 103, 105, 106, 109, 112, 113, 117, 118, 121 }
[3]:  [[78, 59, 5]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[79, 59, 5]] 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 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 0|1 0 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 0 0|0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 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 1 0 0 1 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0|0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0|1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 0 1 0 1 1 1 0|1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 0|0 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0|0 1 0 1 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 0 1 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0|1 1 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0|1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 1 0 1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 1 1 1 0 1 1 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 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0|0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 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 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0|1 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 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 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0|0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 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 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0|1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0|0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 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 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0|1 1 1 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 1 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 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0|1 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 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 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 0|1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 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 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 0|0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]

last modified: 2006-04-03

Notes


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