Bounds on the minimum distance of additive quantum codes

Bounds on [[54,34]]2

lower bound:5
upper bound:7

Construction

Construction of a [[54,34,5]] 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]:  [[54, 34, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 9, 14, 17, 20, 23, 24, 25, 28, 30, 31, 36, 38, 39, 40, 41, 43, 46, 47, 48, 49, 51, 52, 56, 58, 60, 63, 66, 67, 68, 71, 73, 74, 75, 77, 83, 88, 91 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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