Bounds on the minimum distance of additive quantum codes

Bounds on [[22,7]]2

lower bound:5
upper bound:6

Construction

Construction of a [[22,7,5]] quantum code:
[1]:  [[21, 7, 5]] Quantum code over GF(2^2)
     cyclic code of length 21 with generating polynomials [
x^20 + w^2*x^19 + w^2*x^18 + w*x^15 + w^2*x^14 + w^2*x^12 + x^10 + x^9 + w*x^7 + w*x^6 + w*x^5 + 1,
w*x^20 + w^2*x^19 + w*x^18 + x^16 + x^15 + w*x^14 + x^13 + w*x^12 + x^11 + w*x^10 + w^2*x^9 + w
]
[2]:  [[22, 7, 5]] Quantum code over GF(2^2)
     ExtendCode [1] by 1

    stabilizer matrix:

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

last modified: 2005-06-24

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014