Bounds on the minimum distance of additive quantum codes

Bounds on [[73,55]]2

lower bound:5
upper bound:6

Construction

Construction type: DastbastehLisonek

Construction of a [[73,55,5]] quantum code:
[1]:  [[73, 55, 5]] quantum code over GF(2^2)
     cyclic code of length 73 with generating polynomial w*x^72 + w*x^71 + w^2*x^70 + w*x^69 + w*x^68 + w*x^67 + x^66 + w*x^65 + w^2*x^63 + x^62 + w^2*x^61 + x^60 + w^2*x^59 + w*x^58 + x^57 + x^56 + w^2*x^55 + w^2*x^53 + w^2*x^52 + x^51 + w^2*x^50 + w*x^49 + w*x^47 + w*x^46 + w^2*x^44 + x^43 + w*x^42 + x^41 + w*x^40 + w*x^39 + w*x^38 + x^36 + x^35 + w*x^33 + x^32 + x^30 + w*x^28 + x^27 + w^2*x^26 + w*x^24 + x^23 + w*x^22 + w^2*x^21 + x^20 + w*x^19 + w*x^18 + x^15 + w*x^14 + x^13 + x^12 + w^2*x^10 + w^2*x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + w^2*x^3 + w*x^2 + 1

    stabilizer matrix:

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

last modified: 2020-08-24

Notes


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