Bounds on the minimum distance of additive quantum codes

Bounds on [[39,20]]2

lower bound:5
upper bound:7

Construction

Construction of a [[39,20,5]] quantum code:
[1]:  [[35, 20, 5]] Quantum code over GF(2^2)
     cyclic code of length 35 with generating polynomial x^33 + x^30 + x^29 + w*x^28 + w*x^27 + x^26 + x^25 + w^2*x^24 + x^23 + x^22 + w*x^20 + w*x^19 + w^2*x^17 + w^2*x^16 + w*x^14 + w*x^11 + w^2*x^10 + w*x^9 + w*x^8 + 1
[2]:  [[39, 20, 5]] Quantum code over GF(2^2)
     ExtendCode [1] by 4

    stabilizer matrix:

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

last modified: 2006-04-06

Notes


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