Bounds on the minimum distance of additive quantum codes

Bounds on [[45,15]]2

lower bound:8
upper bound:11

Construction

Construction type: QC

Construction of a [[45,15,8]] quantum code:
[1]:  [[45, 15, 8]] Quantum code over GF(2^2)
     quasicyclic code of length 45 stacked to height 2 with 6 generating polynomials

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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