Bounds on the minimum distance of additive quantum codes

Bounds on [[28,19]]2

lower bound:3
upper bound:4

Construction

Construction of a [[28,19,3]] quantum code:
[1]:  [[40, 33, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[26, 19, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 7, 8, 10, 16, 17, 20, 21, 23, 24, 27, 29, 35 }
[3]:  [[27, 19, 3]] quantum code over GF(2^2)
     ExtendCode [2] by 1
[4]:  [[28, 19, 3]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2005-06-27

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014