Bounds on the minimum distance of additive quantum codes

Bounds on [[52,31]]2

lower bound:5
upper bound:7

Construction

Construction of a [[52,31,5]] quantum code:
[1]:  [[93, 73, 5]] quantum code over GF(2^2)
     quasicyclic code of length 93 stacked to height 2 with 6 generating polynomials
[2]:  [[51, 31, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 6, 7, 8, 9, 10, 13, 15, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 35, 39, 42, 45, 46, 49, 50, 52, 57, 60, 61, 64, 73, 74, 76, 77, 79, 85, 86, 88, 90, 92 }
[3]:  [[52, 31, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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