Bounds on the minimum distance of additive quantum codes

Bounds on [[56,35]]2

lower bound:5
upper bound:7

Construction

Construction of a [[56,35,5]] 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]:  [[55, 35, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 6, 8, 12, 13, 15, 16, 19, 20, 21, 25, 26, 32, 33, 34, 35, 37, 40, 42, 45, 46, 47, 48, 51, 52, 55, 56, 60, 63, 64, 68, 69, 80, 82, 86, 87, 89, 90, 93 }
[3]:  [[56, 35, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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