Bounds on the minimum distance of additive quantum codes

Bounds on [[40,3]]2

lower bound:10
upper bound:13

Construction

Construction of a [[40,3,10]] quantum code:
[1]:  [[40, 4, 10]] Quantum code over GF(2^2)
     cyclic code of length 40 with generating polynomial w*x^39 + w*x^38 + w^2*x^37 + x^36 + x^35 + w*x^31 + w*x^30 + w*x^29 + w*x^28 + w^2*x^27 + x^25 + w^2*x^24 + x^23 + w^2*x^22 + x^20 + w^2*x^19 + w^2*x^18 + 1
[2]:  [[40, 3, 10]] 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1|0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 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 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 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 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 0 0 0 0 0 0 1 0|1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 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 0 0 0 0 0 1|0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 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 0 0 0 1 1|1 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 1 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 1 0 0|0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 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 0 0 1 0|0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 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 0 0 1|1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 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 1|0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 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 1 0 0|1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 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 0 0 0 1 0|1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 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 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 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 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 0 0 1 1|0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0|0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0|0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|1 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 1|0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 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 0 1 0 0|1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 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 1 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 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1|1 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0|1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 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 1 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 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1|0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0|1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 1 0|1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1|0 1 1 1 1 0 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 0 0 1 1 1 1 1 1 1 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 0 0 1 0 0 0 0 0 0 0 0 0 1 1|0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0|1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0|0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 0 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 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1|1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1|0 1 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0|1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 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 0 0 0 1 0|1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 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 0 0 1 0 0 0 1|0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 1 1 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 0 0 1 0 1 1|1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 1 0]

last modified: 2006-04-03

Notes


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