Bounds on the minimum distance of additive quantum codes

Bounds on [[41,23]]2

lower bound:5
upper bound:6

Construction

Construction of a [[41,23,5]] quantum code:
[1]:  [[64, 44, 6]] Quantum code over GF(2^2)
     quantum twisted code of length 64 with interval [ 1, 2, 3, 4 ] and parameter kappa 2
[2]:  [[42, 22, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 7, 13, 17, 18, 20, 21, 23, 26, 31, 33, 36, 38, 40, 45, 50, 52, 53, 54, 56, 58, 59, 63 }
[3]:  [[41, 23, 5]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at 42

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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