Bounds on the minimum distance of additive quantum codes

Bounds on [[85,40]]2

lower bound:10
upper bound:15

Construction

Construction of a [[85,40,10]] quantum code:
[1]:  [[85, 41, 10]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomials [
w*x^83 + w^2*x^82 + w^2*x^81 + x^79 + w*x^78 + w*x^77 + w^2*x^76 + w*x^75 + x^74 + w*x^73 + x^72 + x^70 + x^69 + w^2*x^68 + x^67 + x^66 + x^65 + w^2*x^64 + x^63 + w*x^62 + w^2*x^61 + w^2*x^60 + w*x^59 + x^58 + x^57 + w*x^56 + w^2*x^55 + x^53 + w*x^52 + w*x^51 + w^2*x^50 + w^2*x^49 + w^2*x^48 + x^46 + w^2*x^45 + w^2*x^44 + x^43 + x^42 + w^2*x^39 + x^38 + w^2*x^37 + w^2*x^34 + w^2*x^32 + w^2*x^31 + x^30 + x^29 + w^2*x^28 + x^27 + x^26 + x^25 + x^24 + w^2*x^23 + x^22 + 1,
w^2*x^83 + x^82 + x^81 + w*x^79 + w^2*x^78 + w^2*x^77 + x^76 + w^2*x^75 + w*x^74 + w^2*x^73 + w*x^72 + w*x^70 + w*x^69 + x^68 + w*x^67 + w*x^66 + w*x^65 + x^64 + w*x^63 + w^2*x^62 + x^61 + x^60 + w^2*x^59 + w*x^58 + w*x^57 + w^2*x^56 + x^55 + w*x^53 + w^2*x^52 + w^2*x^51 + x^50 + x^49 + x^48 + w*x^46 + x^45 + x^44 + w*x^43 + w*x^42 + x^39 + w*x^38 + x^37 + x^34 + x^32 + x^31 + w*x^30 + w*x^29 + x^28 + w*x^27 + w*x^26 + w*x^25 + w*x^24 + x^23 + w*x^22 + w
]
[2]:  [[85, 40, 10]] quantum code over GF(2^2)
     Subcode of [1]

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