Bounds on the minimum distance of additive quantum codes

Bounds on [[34,18]]2

lower bound:5
upper bound:6

Construction

Construction of a [[34,18,5]] quantum code:
[1]:  [[34, 18, 5]] Quantum code over GF(2^2)
     cyclic code of length 34 with generating polynomial w*x^33 + w^2*x^32 + w^2*x^30 + w*x^28 + w^2*x^26 + w*x^25 + x^24 + w*x^23 + w*x^22 + w*x^20 + w*x^19 + x^18 + w*x^17 + w^2*x^16 + w*x^14 + w^2*x^12 + w^2*x^10 + w*x^9 + x^8 + 1

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


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