Bounds on the minimum distance of additive quantum codes

Bounds on [[39,3]]2

lower bound:10
upper bound:13

Construction

Construction of a [[39,3,10]] quantum code:
[1]:  [[36, 3, 10]] Quantum code over GF(2^2)
     cyclic code of length 36 with generating polynomial w^2*x^35 + w*x^34 + w^2*x^33 + w*x^32 + w^2*x^30 + w^2*x^29 + w^2*x^28 + x^27 + w*x^25 + x^21 + x^19 + x^18 + w*x^17 + w*x^16 + 1
[2]:  [[39, 3, 10]] Quantum code over GF(2^2)
     ExtendCode [1] by 3

    stabilizer matrix:

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