Bounds on the minimum distance of additive quantum codes

Bounds on [[48,33]]2

lower bound:4
upper bound:5

Construction

Construction of a [[48,33,4]] quantum code:
[1]:  [[65, 51, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 65 stacked to height 2 with 10 generating polynomials
[2]:  [[48, 34, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 5, 6, 9, 10, 11, 12, 15, 17, 25, 31, 32, 33, 36, 39, 44, 46, 54 }
[3]:  [[48, 33, 4]] Quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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