Bounds on the minimum distance of additive quantum codes

Bounds on [[63,47]]2

lower bound:4
upper bound:5

Construction

Construction of a [[63,47,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[63, 47, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 4, 5, 7, 12, 14, 15, 19, 20, 21, 24, 33, 36, 45, 48, 49, 50, 69, 70, 76, 78, 80 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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