Bounds on the minimum distance of additive quantum codes

Bounds on [[34,17]]2

lower bound:5
upper bound:6

Construction

Construction of a [[34,17,5]] quantum code:
[1]:  [[34, 17, 5]] Quantum code over GF(2^2)
     cyclic code of length 34 with generating polynomial w^2*x^33 + w^2*x^30 + w^2*x^29 + x^28 + x^27 + w*x^26 + x^24 + w^2*x^23 + x^22 + x^21 + w^2*x^20 + x^19 + w*x^17 + x^16 + x^15 + w^2*x^14 + w^2*x^13 + w^2*x^10 + x^9 + 1

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


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