Bounds on the minimum distance of additive quantum codes

Bounds on [[49,29]]2

lower bound:5
upper bound:7

Construction

Construction of a [[49,29,5]] quantum code:
[1]:  [[93, 73, 5]] quantum code over GF(2^2)
     QuasiCyclicCode of length 93 stacked to height 2 with generating polynomials: x^30 + x^28 + x^27 + x^26 + x^25 + w*x^24 + x^23 + x^20 + x^19 + w^2*x^18 + x^17 + x^16 + w^2*x^14 + w*x^13 + w*x^11 + w^2*x^10 + w^2*x^9 + w^2*x^8 + w^2*x^7 + w*x^5 + w*x^3 + w*x^2,  w*x^27 + x^26 + x^25 + w*x^24 + w*x^23 + w*x^21 + x^20 + x^19 + w*x^18 + w^2*x^16 + x^14 + w^2*x^13 + w*x^10 + w^2*x^8 + x^7 + x^6 + x^5 + w*x^4 + w^2*x^3 + w*x,  w*x^30 + w^2*x^28 + x^27 + w^2*x^26 + x^24 + w^2*x^23 + w*x^22 + w^2*x^19 + x^18 + w*x^17 + w*x^15 + w^2*x^14 + w^2*x^13 + w^2*x^12 + w*x^10 + w^2*x^9 + w^2*x^8 + x^7 + x^6 + x^4 + w^2*x^3 + w*x,  w*x^30 + w*x^28 + w*x^27 + w*x^26 + w*x^25 + w^2*x^24 + w*x^23 + w*x^20 + w*x^19 + x^18 + w*x^17 + w*x^16 + x^14 + w^2*x^13 + w^2*x^11 + x^10 + x^9 + x^8 + x^7 + w^2*x^5 + w^2*x^3 + w^2*x^2,  w^2*x^27 + w*x^26 + w*x^25 + w^2*x^24 + w^2*x^23 + w^2*x^21 + w*x^20 + w*x^19 + w^2*x^18 + x^16 + w*x^14 + x^13 + w^2*x^10 + x^8 + w*x^7 + w*x^6 + w*x^5 + w^2*x^4 + x^3 + w^2*x,  w^2*x^30 + x^28 + w*x^27 + x^26 + w*x^24 + x^23 + w^2*x^22 + x^19 + w*x^18 + w^2*x^17 + w^2*x^15 + x^14 + x^13 + x^12 + w^2*x^10 + x^9 + x^8 + w*x^7 + w*x^6 + w*x^4 + x^3 + w^2*x
[2]:  [[49, 29, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 6, 9, 10, 12, 16, 17, 18, 20, 21, 22, 23, 25, 29, 31, 32, 33, 35, 37, 38, 42, 43, 47, 49, 53, 57, 62, 63, 64, 65, 66, 68, 72, 74, 76, 78, 80, 83, 84, 86, 90, 91, 92 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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