Bounds on the minimum distance of additive quantum codes

Bounds on [[36,0]]2

lower bound:12
upper bound:14

Construction

Construction of a [[36,0,12]] quantum code:
[1]:  [[36, 0, 12]] self-dual Quantum code over GF(2^2)
     quasicyclic code of length 36 stacked to height 2 with 4 generating polynomials

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

last modified: 2006-04-06

Notes


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