Bounds on the minimum distance of additive quantum codes

Bounds on [[60,39]]2

lower bound:5
upper bound:7

Construction

Construction of a [[60,39,5]] 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]:  [[59, 39, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 6, 13, 20, 21, 25, 29, 31, 33, 34, 35, 38, 39, 44, 45, 47, 48, 52, 60, 61, 63, 64, 68, 72, 74, 76, 77, 78, 79, 80, 87 }
[3]:  [[60, 39, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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