Bounds on the minimum distance of additive quantum codes

Bounds on [[51,28]]2

lower bound:6
upper bound:8

Construction

Construction of a [[51,28,6]] quantum code:
[1]:  [[64, 44, 6]] Quantum code over GF(2^2)
     quantum twisted code of length 64 with interval [ 1, 2, 3, 4 ] and parameter kappa 2
[2]:  [[48, 28, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 13, 22, 23, 32, 34, 39, 43, 47, 48, 51, 53, 54, 56, 60, 62, 63 }
[3]:  [[51, 28, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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