Bounds on the minimum distance of additive quantum codes

Bounds on [[45,24]]2

lower bound:6
upper bound:8

Construction

Construction of a [[45,24,6]] quantum code:
[1]:  [42, 10] Quasicyclic of degree 2 Linear Code over GF(2^2)
     QuasiCyclicCode of length 42 stacked to height  2 with generating polynomials: x^12 + w*x^11 + w*x^10 + w*x^9 + w^2*x^7 + w^2*x^6 + x^5 + w*x^3 + w^2*x^2 + x + 1,  x^19 + w*x^18 + w*x^16 + w^2*x^14 + w^2*x^12 + x^11 + w^2*x^10 + w^2*x^9 + x^8 + w*x^6 + x^5 + w^2*x^4 + w^2,  0,  x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1
[2]:  [[44, 24, 6]] quantum code over GF(2^2)
     QuantumConstructionX applied to [1] with e = 2
[3]:  [[45, 24, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2024-06-15

Notes


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