Bounds on the minimum distance of additive quantum codes

Bounds on [[43,23]]2

lower bound:5
upper bound:7

Construction

Construction of a [[43,23,5]] quantum code:
[1]:  [[42, 24, 5]] quantum code over GF(2^2)
     QuasiCyclicCode of length 42 stacked to height 2 with generating polynomials: w*x^18 + w*x^17 + w^2*x^15 + w*x^14 + w*x^13 + x^11 + x^9 + w*x^8 + x^7 + w*x^6 + x^5 + x^4 + w^2*x^3 + w*x^2 + w*x + 1,  w^2*x^18 + w^2*x^16 + x^15 + w*x^14 + w^2*x^13 + w^2*x^11 + w^2*x^9 + w*x^8 + w^2*x^7 + w*x^6 + x^5 + w^2*x^4 + w*x^2 + w^2,  w^2*x^18 + w^2*x^17 + x^15 + w^2*x^14 + w^2*x^13 + w*x^11 + w*x^9 + w^2*x^8 + w*x^7 + w^2*x^6 + w*x^5 + w*x^4 + x^3 + w^2*x^2 + w^2*x + w,  x^18 + x^16 + w*x^15 + w^2*x^14 + x^13 + x^11 + x^9 + w^2*x^8 + x^7 + w^2*x^6 + w*x^5 + x^4 + w^2*x^2 + 1
[2]:  [[42, 23, 5]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[43, 23, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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