Bounds on the minimum distance of additive quantum codes

Bounds on [[55,47]]2

lower bound:3
upper bound:3

Construction

Construction of a [[55,47,3]] quantum code:
[1]:  [[85, 77, 3]] Quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial w*x^84 + w^2*x^83 + w^2*x^81 + w^2*x^79 + w*x^78 + w^2*x^76 + w*x^74 + w^2*x^72 + w^2*x^71 + w^2*x^70 + w*x^69 + w^2*x^68 + x^67 + w^2*x^66 + w*x^64 + x^63 + x^62 + w^2*x^60 + x^59 + w^2*x^58 + w*x^57 + x^56 + x^54 + x^53 + w^2*x^52 + w*x^49 + w*x^46 + x^45 + w*x^44 + x^43 + x^42 + x^41 + x^40 + w*x^39 + w^2*x^38 + x^37 + x^36 + w^2*x^35 + w^2*x^34 + x^33 + w*x^30 + w*x^29 + w^2*x^28 + w^2*x^27 + x^26 + w^2*x^25 + x^24 + w*x^22 + x^21 + w^2*x^20 + w^2*x^19 + w*x^18 + x^17 + w*x^16 + w*x^15 + w^2*x^13 + x^12 + w^2*x^10 + w^2*x^9 + w^2*x^7 + x^6 + x^5 + x^4 + 1
[2]:  [[55, 47, 3]] Quantum code over GF(2^2)
     Shortening of [1] at { 5, 7, 9, 11, 12, 13, 14, 18, 21, 23, 28, 29, 30, 32, 34, 36, 37, 43, 44, 47, 57, 60, 61, 62, 64, 69, 70, 76, 83, 85 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014