Bounds on the minimum distance of additive quantum codes

Bounds on [[55,39]]2

lower bound:4
upper bound:6

Construction

Construction of a [[55,39,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[55, 39, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 4, 7, 8, 9, 12, 18, 21, 23, 27, 28, 29, 33, 35, 36, 39, 48, 51, 56, 58, 59, 60, 62, 63, 64, 66, 71, 73, 75, 81, 82 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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