Bounds on the minimum distance of additive quantum codes

Bounds on [[55,28]]2

lower bound:6
upper bound:9

Construction

Construction of a [[55,28,6]] quantum code:
[1]:  [[54, 30, 6]] Quantum code over GF(2^2)
     quasicyclic code of length 54 with 1 generating polynomials
[2]:  [[54, 28, 6]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[55, 28, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

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

last modified: 2006-04-03

Notes


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