Bounds on the minimum distance of additive quantum codes

Bounds on [[54,32]]2

lower bound:5
upper bound:8

Construction

Construction of a [[54,32,5]] 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]:  [[52, 32, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 4, 9, 10, 13, 14, 17, 18, 19, 21, 22, 27, 29, 30, 33, 34, 35, 36, 42, 44, 45, 48, 53, 58, 59, 64, 65, 70, 72, 73, 75, 77, 78, 83, 84, 87, 88, 91, 92, 93 }
[3]:  [[54, 32, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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