Bounds on the minimum distance of additive quantum codes

Bounds on [[47,27]]2

lower bound:5
upper bound:7

Construction

Construction of a [[47,27,5]] quantum code:
[1]:  [[93, 73, 5]] Quantum code over GF(2^2)
     quasicyclic code of length 93 stacked to height 2 with 6 generating polynomials
[2]:  [[47, 27, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 5, 7, 9, 13, 15, 16, 18, 21, 22, 29, 31, 35, 38, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 56, 60, 63, 66, 67, 68, 69, 70, 71, 73, 75, 77, 78, 80, 82, 84, 85, 86, 88, 91, 93 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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