Bounds on the minimum distance of additive quantum codes

Bounds on [[52,38]]2

lower bound:4
upper bound:5

Construction

Construction of a [[52,38,4]] quantum code:
[1]:  [[52, 38, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 52 stacked to height 2 with 8 generating polynomials

    stabilizer matrix:

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