Bounds on the minimum distance of additive quantum codes

Bounds on [[33,20]]2

lower bound:4
upper bound:5

Construction

Construction of a [[33,20,4]] quantum code:
[1]:  [[40, 30, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 40 stacked to height 2 with 16 generating polynomials
[2]:  [[30, 20, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 11, 13, 27, 29, 37, 40 }
[3]:  [[32, 20, 4]] Quantum code over GF(2^2)
     ExtendCode [2] by 2
[4]:  [[33, 20, 4]] Quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


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