Bounds on the minimum distance of additive quantum codes

Bounds on [[28,10]]2

lower bound:6
upper bound:7

Construction

Construction of a [[28,10,6]] quantum code:
[1]:  [[28, 10, 6]] Quantum code over GF(2^2)
     cyclic code of length 28 with generating polynomial x^27 + w*x^26 + w*x^25 + w^2*x^24 + x^22 + w^2*x^21 + x^20 + x^18 + w^2*x^16 + w^2*x^14 + w*x^13 + x^12 + w*x^11 + w^2*x^9 + w

    stabilizer matrix:

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

last modified: 2005-06-27

Notes


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