Bounds on the minimum distance of additive quantum codes

Bounds on [[28,18]]2

lower bound:4
upper bound:4

Construction

Construction of a [[28,18,4]] quantum code:
[1]:  [[40, 30, 4]] quantum code over GF(2^2)
     quasicyclic code of length 40 stacked to height 2 with 16 generating polynomials
[2]:  [[28, 18, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 5, 7, 9, 12, 13, 15, 16, 28, 34, 35, 37 }

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


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