Bounds on the minimum distance of additive quantum codes

Bounds on [[53,33]]2

lower bound:5
upper bound:7

Construction

Construction of a [[53,33,5]] quantum code:
[1]:  [[93, 73, 5]] Quantum code over GF(2^2)
     quasicyclic code of length 93 stacked to height 2 with 6 generating polynomials
[2]:  [[53, 33, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 5, 8, 9, 16, 18, 20, 23, 25, 27, 31, 38, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 57, 58, 59, 60, 63, 66, 68, 70, 74, 76, 77, 79, 82, 83, 90, 92 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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