Bounds on the minimum distance of additive quantum codes

Bounds on [[45,31]]2

lower bound:4
upper bound:5

Construction

Construction of a [[45,31,4]] quantum code:
[1]:  [[65, 51, 4]] quantum code over GF(2^2)
     quasicyclic code of length 65 stacked to height 2 with 10 generating polynomials
[2]:  [[45, 31, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 6, 10, 13, 22, 24, 29, 30, 31, 38, 42, 44, 49, 52, 53, 55, 57, 62, 64, 65 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014