Bounds on the minimum distance of additive quantum codes

Bounds on [[59,43]]2

lower bound:4
upper bound:5

Construction

Construction of a [[59,43,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[59, 43, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 18, 19, 21, 25, 26, 30, 32, 33, 39, 40, 43, 47, 50, 51, 57, 58, 60, 63, 65, 66, 70, 71, 79, 80, 82, 85 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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