Bounds on the minimum distance of additive quantum codes

Bounds on [[41,19]]2

lower bound:6
upper bound:8

Construction

Construction of a [[41,19,6]] quantum code:
[1]:  [[41, 21, 6]] Quantum code over GF(2^2)
     cyclic code of length 41 with generating polynomial w^2*x^40 + x^39 + w*x^38 + x^37 + w^2*x^35 + x^34 + w^2*x^33 + x^32 + x^31 + x^29 + w*x^28 + w*x^27 + w^2*x^26 + w^2*x^25 + w*x^24 + w*x^23 + x^22 + x^20 + x^19 + w^2*x^18 + x^17 + w^2*x^16 + x^14 + w*x^13 + x^12 + w^2*x^11 + x^10 + 1
[2]:  [[41, 19, 6]] Quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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