Bounds on the minimum distance of additive quantum codes

Bounds on [[28,11]]2

lower bound:6
upper bound:7

Construction

Construction of a [[28,11,6]] quantum code:
[1]:  [[28, 12, 6]] Quantum code over GF(2^2)
     V. D. Tonchev
Construction from a stored generator matrix
[2]:  [[28, 11, 6]] Quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

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

last modified: 2010-07-16

Notes


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