Bounds on the minimum distance of additive quantum codes

Bounds on [[35,0]]2

lower bound:11
upper bound:13

Construction

Construction of a [[35,0,11]] 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
[2]:  [[35, 1, 11]] Quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 36
[3]:  [[35, 0, 11]] self-dual Quantum code over GF(2^2)
     Subcode of [2]

    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|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 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 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 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 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 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 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 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 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 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|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]
      [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 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]
      [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 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 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 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 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 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 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 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]
      [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 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]
      [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 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 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 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 1 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]
      [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|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]
      [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 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 1 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]
      [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 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 1 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 1 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]
      [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|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]
      [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 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]
      [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 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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]
      [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 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 1 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]
      [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|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 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: 2005-07-05

Notes


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