Bounds on the minimum distance of additive quantum codes

Bounds on [[21,6]]2

lower bound:5
upper bound:6

Construction

Construction of a [[21,6,5]] quantum code:
[1]:  [[18, 6, 5]] quantum code over GF(2^2)
     QuasiCyclicCode of length 18 stacked to height 2 with generating polynomials: x^5 + x^4,  x^5 + x^3 + x^2 + w*x,  w^2*x^5 + w^2*x^4 + w*x^3 + w^2*x,  w*x^5 + w*x^4,  w*x^5 + w*x^3 + w*x^2 + w^2*x,  x^5 + x^4 + w^2*x^3 + x
[2]:  [[21, 6, 5]] quantum code over GF(2^2)
     ExtendCode [1] by 3

    stabilizer matrix:

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

last modified: 2005-06-24

Notes


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