Bounds on the minimum distance of additive quantum codes

Bounds on [[30,10]]2

lower bound:6
upper bound:8

Construction

Construction of a [[30,10,6]] quantum code:
[1]:  [[30, 11, 6]] Quantum code over GF(2^2)
     cyclic code of length 30 with generating polynomial w*x^28 + w^2*x^27 + w^2*x^26 + w*x^25 + x^24 + w^2*x^23 + w*x^22 + x^20 + w*x^19 + x^18 + w^2*x^16 + w*x^14 + w*x^13 + w^2*x^12 + w^2*x^11 + x^10 + w*x^9 + w
[2]:  [[30, 10, 6]] Quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

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

last modified: 2005-06-24

Notes


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