Bounds on the minimum distance of additive quantum codes

Bounds on [[63,36]]2

lower bound:7
upper bound:9

Construction

Construction type: GraQC

Construction of a [[63,36,7]] quantum code:
[1]:  [[63, 36, 7]] quantum code over GF(2^2)
     quasicyclic code of length 63 stacked to height 2 with 2 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 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1|0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0|0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0|0 0 0 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 1 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 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1|0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 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 1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1|0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0|0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 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 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1|0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 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 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0|0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 0 1]
      [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 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 1 1|0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0|0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0|0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 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 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1|0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1|0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 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 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 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 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1|0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 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 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 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 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 1 1 0 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 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1|0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 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 0 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1|0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 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 1 1 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1|0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 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 0 0 0 0 0 0 0 0 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 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1]

last modified: 2020-09-17

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014