Bounds on the minimum distance of additive quantum codes

Bounds on [[60,40]]2

lower bound:5
upper bound:6

Construction

Construction of a [[60,40,5]] 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]:  [[60, 40, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 4, 5, 7, 13, 14, 16, 18, 20, 23, 32, 37, 41, 44, 47, 48, 51, 52, 54, 59, 62, 63, 66, 75, 76, 78, 79, 81, 87, 88, 90, 92 }

    stabilizer matrix:

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