Bounds on the minimum distance of additive quantum codes

Bounds on [[82,59]]2

lower bound:6
upper bound:7

Construction

Construction of a [[82,59,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[82, 59, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 5, 7, 8, 15, 16, 18, 19, 21, 22, 23, 34, 35, 36, 37, 40, 43, 48, 49, 51, 53, 61, 66, 68, 69, 70, 74, 75, 82, 85, 86, 88, 98, 103, 104, 105, 106, 108, 112, 115, 118, 120, 121, 126, 128 }

    stabilizer matrix:

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