Bounds on the minimum distance of additive quantum codes

Bounds on [[29,0]]2

lower bound:11
upper bound:11

Construction

Construction of a [[29,0,11]] quantum code:
[1]:  [[29, 0, 11]] self-dual Quantum code over GF(2^2)
     cyclic code of length 29 with generating polynomial w^2*x^27 + w*x^26 + x^23 + w^2*x^22 + x^19 + w^2*x^18 + w^2*x^17 + w*x^16 + w*x^15 + w*x^14 + 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 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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|1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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|1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 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|0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 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 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 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 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 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 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 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|1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 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 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 0 1 1 1 0 1 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 0 0 0 0 0 0|1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 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|1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 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|1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 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 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 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|1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 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|1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 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|0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 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|1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 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|1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 0 0 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|1 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0|0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0 0|1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0 0|0 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0 0|0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0 0|0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 0 0|0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0 0|1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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 1 0|1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 1|0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 0 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