Bounds on the minimum distance of additive quantum codes

Bounds on [[80,61]]2

lower bound:5
upper bound:6

Construction

Construction of a [[80,61,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[80, 62, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 5, 8, 11, 13, 15, 17, 22, 23, 26, 27, 28, 30, 35, 40, 45, 50, 51, 54, 55, 58, 59, 61, 65, 66, 67, 71, 76, 78, 81, 86, 90, 92, 95, 97, 98, 99, 100, 111, 116, 121 }
[3]:  [[80, 61, 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 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0|0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 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 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 1|0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1|1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0|1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0|1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 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 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 0 0 1|0 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1]
      [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0|0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1]
      [0 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 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 1 1 0 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0|1 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 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 1 1 0 0 0 1 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 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1|1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 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 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0|0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 0 1 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 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1|0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 0 1 0 0|1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0|1 0 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 0|0 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 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 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 1|0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 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 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 1 1 1|0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 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 1 1 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1|0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1]

last modified: 2006-04-03

Notes


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