Bounds on the minimum distance of additive quantum codes

Bounds on [[82,61]]2

lower bound:5
upper bound:6

Construction

Construction of a [[82,61,5]] 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]:  [[82, 61, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 1, 2, 4, 6, 7, 9, 10, 13, 16, 18, 20, 21, 23, 24, 26, 29, 30, 34, 35, 38, 42, 43, 46, 48, 59, 65, 71, 73, 76, 78, 82, 89, 92, 94, 95, 96, 98, 105, 110, 111, 113, 116, 119, 122, 124 }

    stabilizer matrix:

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