Bounds on the minimum distance of additive quantum codes

Bounds on [[65,51]]2

lower bound:4
upper bound:4

Construction

Construction of a [[65,51,4]] 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

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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