Bounds on the minimum distance of additive quantum codes

Bounds on [[27,12]]2

lower bound:5
upper bound:6

Construction

Construction of a [[27,12,5]] quantum code:
[1]:  [[26, 12, 5]] quantum code over GF(2^2)
     QuasiCyclicCode of length 26 stacked to height 2 with generating polynomials: x^12 + w*x^11 + w^2*x^8 + x^7 + w*x^6 + w^2*x^5 + x^4 + w^2*x^3 + w*x^2 + w*x + 1,  w^2*x^12 + w*x^11 + x^10 + w^2*x^8 + x^6 + w*x^4 + w*x^3 + x^2 + 1,  w*x^12 + w^2*x^11 + x^8 + w*x^7 + w^2*x^6 + x^5 + w*x^4 + x^3 + w^2*x^2 + w^2*x + w,  x^12 + w^2*x^11 + w*x^10 + x^8 + w*x^6 + w^2*x^4 + w^2*x^3 + w*x^2 + w
[2]:  [[27, 12, 5]] quantum code over GF(2^2)
     ExtendCode [1] by 1

    stabilizer matrix:

      [1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 0|0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0|1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0]
      [0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0|0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0]
      [0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0|0 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0]
      [0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0|0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0]
      [0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0|0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0]
      [0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0|0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0]
      [0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0|0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0]
      [0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 1 0 1 0|0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0]
      [0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0|0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0]
      [0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0]
      [0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0|0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0]
      [0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0|0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0|0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 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 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: 2005-06-27

Notes


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