Bounds on the minimum distance of additive quantum codes

Bounds on [[45,22]]2

lower bound:6
upper bound:8

Construction

Construction of a [[45,22,6]] quantum code:
[1]:  [[46, 22, 7]] quantum code over GF(2^2)
     QuasiCyclicCode of length 46 stacked to height 2 with generating polynomials: x^22 + w*x^21 + x^20 + w*x^19 + w^2*x^18 + x^17 + w*x^16 + w^2*x^15 + w*x^14 + x^13 + w*x^11 + w^2*x^9 + w*x^8 + w*x^7 + x^6 + x^5 + x^3 + w^2*x^2 + 1,  w^2*x^22 + w^2*x^20 + w^2*x^18 + x^17 + x^16 + x^14 + w^2*x^12 + w*x^11 + w*x^9 + w*x^7 + w^2*x^5 + x^4 + w^2*x^3 + w^2*x^2 + w^2,  w*x^22 + w^2*x^21 + w*x^20 + w^2*x^19 + x^18 + w*x^17 + w^2*x^16 + x^15 + w^2*x^14 + w*x^13 + w^2*x^11 + x^9 + w^2*x^8 + w^2*x^7 + w*x^6 + w*x^5 + w*x^3 + x^2 + w,  x^22 + x^20 + x^18 + w*x^17 + w*x^16 + w*x^14 + x^12 + w^2*x^11 + w^2*x^9 + w^2*x^7 + x^5 + w*x^4 + x^3 + x^2 + 1
[2]:  [[45, 22, 6]] quantum code over GF(2^2)
     Puncturing of [1] at { 46 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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