Bounds on the minimum distance of additive quantum codes

Bounds on [[15,0]]2

lower bound:6
upper bound:6

Construction

Construction of a [[15,0,6]] quantum code:
[1]:  [[15, 0, 6]] self-dual Quantum code over GF(2^2)
     cyclic code of length 15 with generating polynomial x^14 + w^2*x^13 + w^2*x^12 + x^11 + w^2*x^10 + w^2*x^9 + x^8 + w*x^7 + w

    stabilizer matrix:

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