Bounds on the minimum distance of additive quantum codes

Bounds on [[62,45]]2

lower bound:5
upper bound:6

Construction

Construction of a [[62,45,5]] quantum code:
[1]:  [[62, 46, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[62, 45, 5]] Quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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