Bounds on the minimum distance of additive quantum codes

Bounds on [[72,56]]2

lower bound:4
upper bound:5

Construction

Construction of a [[72,56,4]] quantum code:
[1]:  [[90, 74, 4]] quantum code over GF(2^2)
     quasicyclic code of length 90 stacked to height 2 with 12 generating polynomials
[2]:  [[72, 56, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 4, 16, 17, 22, 25, 29, 36, 48, 52, 66, 67, 73, 74, 75, 76, 80, 86 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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