Bounds on the minimum distance of additive quantum codes

Bounds on [[39,16]]2

lower bound:6
upper bound:8

Construction

Construction of a [[39,16,6]] quantum code:
[1]:  [[34, 16, 6]] Quantum code over GF(2^2)
     cyclic code of length 34 with generating polynomial x^32 + x^31 + w^2*x^30 + w*x^29 + w^2*x^28 + w^2*x^27 + w*x^25 + w^2*x^24 + w^2*x^23 + x^20 + w*x^19 + w^2*x^18 + x^16 + w*x^15 + w^2*x^14 + w*x^13 + w*x^12 + w^2*x^11 + w^2*x^9 + 1
[2]:  [[35, 16, 6]] Quantum code over GF(2^2)
     ExtendCode [1] by 1
[3]:  [[39, 16, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 4

    stabilizer matrix:

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

last modified: 2006-04-07

Notes


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