Bounds on the minimum distance of additive quantum codes

Bounds on [[14,0]]2

lower bound:6
upper bound:6

Construction

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

    stabilizer matrix:

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

last modified: 2006-04-17

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 10.06.2024