Bounds on the minimum distance of additive quantum codes

Bounds on [[39,17]]2

lower bound:6
upper bound:8

Construction

Construction of a [[39,17,6]] 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]:  [[38, 18, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 3, 11, 12, 17, 19, 21, 25, 27, 30, 31, 32, 33, 35, 38, 40, 41, 42, 45, 46, 48, 50, 52, 54, 59, 60, 64 }
[3]:  [[38, 17, 6]] Quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[39, 17, 6]] Quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2006-04-07

Notes


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