Bounds on the minimum distance of additive quantum codes

Bounds on [[59,47]]2

lower bound:4
upper bound:4

Construction

Construction of a [[59,47,4]] quantum code:
[1]:  [[85, 73, 4]] Quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomial w*x^84 + w^2*x^83 + w*x^81 + w*x^80 + x^79 + w^2*x^78 + w*x^76 + x^75 + w*x^74 + x^73 + x^71 + w^2*x^70 + w^2*x^69 + w*x^67 + w*x^66 + w^2*x^65 + x^64 + w^2*x^63 + x^62 + w*x^61 + w^2*x^60 + x^59 + w*x^57 + w^2*x^55 + w*x^54 + w*x^53 + w^2*x^52 + x^51 + x^50 + x^49 + w*x^48 + x^47 + w*x^46 + w*x^45 + x^44 + w*x^43 + x^42 + x^41 + x^40 + w^2*x^39 + w*x^38 + w*x^37 + w^2*x^36 + w*x^34 + x^32 + w^2*x^31 + w*x^30 + x^29 + w^2*x^28 + x^27 + w^2*x^26 + w*x^25 + w*x^24 + w^2*x^22 + w^2*x^21 + x^20 + x^18 + w*x^17 + x^16 + w*x^15 + w^2*x^13 + x^12 + w*x^11 + w*x^10 + w^2*x^8 + w*x^7 + x^6 + 1
[2]:  [[59, 47, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 7, 8, 20, 22, 25, 27, 30, 32, 33, 36, 37, 39, 51, 57, 58, 59, 61, 64, 66, 67, 71, 74, 76, 85 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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