Bounds on the minimum distance of additive quantum codes

Bounds on [[46,24]]2

lower bound:6
upper bound:8

Construction

Construction of a [[46,24,6]] quantum code:
[1]:  [[92, 70, 5]] Quantum code over GF(2^2)
     quasicyclic code of length 92 stacked to height 2 with 8 generating polynomials
[2]:  [[46, 24, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69 }

    stabilizer matrix:

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