Bounds on the minimum distance of additive quantum codes

Bounds on [[55,32]]2

lower bound:5
upper bound:8

Construction

Construction of a [[55,32,5]] quantum code:
[1]:  [[58, 30, 6]] Quantum code over GF(2^2)
     quasicyclic code of length 58 with 1 generating polynomials
[2]:  [[55, 33, 5]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 1, 4, 30 }
[3]:  [[55, 32, 5]] Quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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