Bounds on the minimum distance of additive quantum codes

Bounds on [[46,34]]2

lower bound:4
upper bound:4

Construction

Construction of a [[46,34,4]] quantum code:
[1]:  [[62, 50, 4]] quantum code over GF(2^2)
     quasicyclic code of length 62 stacked to height 2 with 4 generating polynomials
[2]:  [[46, 34, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 6, 10, 13, 15, 18, 20, 21, 22, 25, 28, 33, 41, 48, 49, 58 }

    stabilizer matrix:

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