Bounds on the minimum distance of additive quantum codes

Bounds on [[30,22]]2

lower bound:3
upper bound:3

Construction

Construction of a [[30,22,3]] quantum code:
[1]:  [[40, 33, 3]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[29, 22, 3]] Quantum code over GF(2^2)
     Shortening of [1] at { 5, 11, 19, 22, 23, 24, 27, 29, 32, 33, 38 }
[3]:  [[30, 22, 3]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2005-06-29

Notes


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