Bounds on the minimum distance of additive quantum codes

Bounds on [[19,0]]2

lower bound:7
upper bound:7

Construction

Construction of a [[19,0,7]] quantum code:
[1]:  [[19, 0, 7]] self-dual Quantum code over GF(2^2)
     cyclic code of length 19 with generating polynomial w^2*x^18 + w*x^16 + x^15 + w*x^14 + w^2*x^12 + w*x^11 + w

    stabilizer matrix:

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

last modified: 2006-04-17

Notes


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