Bounds on the minimum distance of additive quantum codes

Bounds on [[39,26]]2

lower bound:4
upper bound:5

Construction

Construction of a [[39,26,4]] quantum code:
[1]:  [[39, 27, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 39 with 2 generating polynomials
[2]:  [[39, 26, 4]] 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 1 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0|1 1 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 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 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0|1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 0 1 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0|0 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1|1 0 0 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0|1 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0|0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 0 1 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 0 0 0 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 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1|0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0|0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 0|1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0|1 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1|0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0|1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1]

last modified: 2006-04-06

Notes


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