Bounds on the minimum distance of additive quantum codes

Bounds on [[59,36]]2

lower bound:5
upper bound:8

Construction

Construction of a [[59,36,5]] quantum code:
[1]:  [[62, 32, 7]] quantum code over GF(2^2)
     quasicyclic code of length 62 stacked to height 2 with 4 generating polynomials
[2]:  [[58, 36, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 1, 17, 32, 37 }
[3]:  [[59, 36, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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