Bounds on the minimum distance of additive quantum codes

Bounds on [[55,22]]2

lower bound:8
upper bound:12

Construction

Construction of a [[55,22,8]] quantum code:
[1]:  [[54, 24, 8]] Quantum code over GF(2^2)
     Code found by Petr Lisonek and Vijaykumar Singh 
Construction from a stored generator matrix
[2]:  [[54, 22, 8]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[55, 22, 8]] 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 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0|0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 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 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0|0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 0|0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 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 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 0|0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 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 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0|0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0|0 0 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 0 0 0 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 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0|0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 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 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 0 0|0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 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 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0|0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 0 1 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 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0|0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 0 1 0 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 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 0|0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 0 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 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0|0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 0 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 1 1 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0|0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 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 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0|0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 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 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0|0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 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 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 1 1 1 1 0 0 0 1 0 0 0 0|0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 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 1 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0|0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 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 1 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 1 1 0|0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 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 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 0|0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 1 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 0 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 0 1 0 0 0 0 1 0 0|0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0|0 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 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 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0|0 0 0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 0 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 0 0 0 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 0|0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 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 1 0 0 0 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0|0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 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 1 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0|0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 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 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0|0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 0 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 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0|0 0 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 1 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 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0|0 0 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 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 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0|0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 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 0 0 0 0 0 0 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|0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 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 0 0 0 0 0 0 0 0 0 0 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]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 0 0 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 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 1 0 0]

last modified: 2013-12-09

Notes


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