Bounds on the minimum distance of additive quantum codes

Bounds on [[111,86]]2

lower bound:5
upper bound:8

Construction

Construction of a [[111,86,5]] quantum code:
[1]:  [[113, 85, 7]] quantum code over GF(2^2)
     cyclic code of length 113 with generating polynomial w*x^111 + x^110 + w^2*x^108 + w*x^107 + w*x^106 + w*x^105 + w^2*x^103 + x^102 + x^101 + x^100 + w*x^99 + w*x^98 + x^97 + w*x^96 + w^2*x^94 + x^92 + w^2*x^91 + w*x^89 + x^88 + w^2*x^87 + w^2*x^86 + x^85 + w*x^84 + w^2*x^83 + w*x^81 + w*x^80 + w^2*x^79 + w*x^78 + w*x^77 + w*x^75 + w*x^74 + w*x^73 + x^72 + w*x^70 + w^2*x^67 + w*x^65 + w*x^64 + w*x^63 + w*x^62 + w^2*x^60 + w*x^57 + x^55 + w*x^54 + w*x^53 + w*x^52 + w*x^50 + w*x^49 + w^2*x^48 + w*x^47 + w*x^46 + w^2*x^44 + w*x^43 + x^42 + w^2*x^41 + w^2*x^40 + x^39 + w*x^38 + w^2*x^36 + x^35 + w^2*x^33 + w*x^31 + x^30 + w*x^29 + w*x^28 + x^27 + x^26 + x^25 + w^2*x^24 + w*x^22 + w*x^21 + w*x^20 + w^2*x^19 + x^17 + w*x^16 + x^14 + 1
[2]:  [[111, 87, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 112, 113 }
[3]:  [[111, 86, 5]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [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 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 0 0|1 1 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 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 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0|0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 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 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1|0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 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 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 0 1|1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 0 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 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0|0 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 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 0 1 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 0|0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 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 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 0|1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1]
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      [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 1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 1 1 1|1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 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 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1|1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 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 1 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1|1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 0 1 1]
      [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 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1|1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1]
      [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 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 0 1 1 1 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 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 0 0 1 1 1 0 1 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 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 0|0 1 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1]
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      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1|0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0]
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last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014