Bounds on the minimum distance of additive quantum codes

Bounds on [[31,0]]2

lower bound:10
upper bound:12

Construction

Construction of a [[31,0,10]] quantum code:
[1]:  [[31, 0, 10]] self-dual Quantum code over GF(2^2)
     cyclic code of length 31 with generating polynomial x^30 + w^2*x^29 + w*x^28 + w^2*x^27 + w*x^25 + x^23 + w*x^21 + w^2*x^19 + w*x^18 + w^2*x^17 + x^16 + 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 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 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|1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 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|0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 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|1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 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 0 0 0 0|1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1]
      [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|1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1]
      [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|1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 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 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 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|1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0|0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0|0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0|1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 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 0 0 0|0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 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 0 0|0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 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 0|1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 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 0|1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 0 0 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 0|1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0|1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 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 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 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 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1]
      [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 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0 0|0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0 0|0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 1 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 1 0 0 0 0 0 0 0|1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 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 1 0 0 0 0 0 0|0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 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 1 0 0 0 0 0|1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 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 1 0 0 0 0|1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 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|1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 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 1 0 0|1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 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 1 0|0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 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 1|1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0]

last modified: 2005-06-27

Notes


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