Bounds on the minimum distance of additive quantum codes

Bounds on [[30,0]]2

lower bound:12
upper bound:12

Construction

Construction of a [[30,0,12]] quantum code:
[1]:  [[30, 0, 12]] self-dual Quantum code over GF(2^2)
     cyclic code of length 30 with generating polynomial w*x^29 + w^2*x^28 + w^2*x^27 + x^26 + w^2*x^25 + w*x^24 + w*x^23 + x^22 + w^2*x^21 + w*x^20 + w*x^19 + w*x^18 + x^17 + x^16 + w*x^15 + 1

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

last modified: 2006-04-17

Notes


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