Bounds on the minimum distance of additive quantum codes

Bounds on [[13,0]]2

lower bound:5
upper bound:5

Construction

Construction of a [[13,0,5]] quantum code:
[1]:  [[13, 0, 5]] self-dual Quantum code over GF(2^2)
     cyclic code of length 13 with generating polynomial w^2*x^12 + x^11 + x^10 + w*x^9 + w^2*x^8 + w*x^6 + 1

    stabilizer matrix:

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

last modified: 2006-04-17

Notes


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