Bounds on the minimum distance of additive quantum codes

Bounds on [[38,14]]2

lower bound:6
upper bound:9

Construction

Construction of a [[38,14,6]] quantum code:
[1]:  [[32, 15, 6]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[32, 14, 6]] Quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[35, 14, 6]] Quantum code over GF(2^2)
     ExtendCode [2] by 3
[4]:  [[38, 14, 6]] Quantum code over GF(2^2)
     ExtendCode [3] by 3

    stabilizer matrix:

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

last modified: 2006-04-07

Notes


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