Bounds on the minimum distance of additive quantum codes

Bounds on [[85,28]]2

lower bound:13
upper bound:20

Construction

Construction of a [[85,28,13]] quantum code:
[1]:  [[85, 29, 13]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomials [
w^2*x^81 + w^2*x^80 + x^79 + w^2*x^78 + x^77 + x^76 + w^2*x^75 + x^74 + w^2*x^71 + w*x^70 + x^68 + w^2*x^67 + x^66 + x^64 + w^2*x^63 + w*x^62 + w^2*x^61 + w^2*x^60 + x^59 + w*x^58 + x^57 + x^56 + x^55 + w*x^54 + w^2*x^53 + x^52 + w^2*x^51 + w*x^50 + w^2*x^49 + w*x^48 + w^2*x^47 + w*x^43 + w^2*x^41 + w^2*x^40 + w*x^39 + w^2*x^37 + x^36 + w*x^35 + x^33 + w^2*x^31 + w*x^30 + w^2*x^29 + x^28 + 1,
x^81 + x^80 + w*x^79 + x^78 + w*x^77 + w*x^76 + x^75 + w*x^74 + x^71 + w^2*x^70 + w*x^68 + x^67 + w*x^66 + w*x^64 + x^63 + w^2*x^62 + x^61 + x^60 + w*x^59 + w^2*x^58 + w*x^57 + w*x^56 + w*x^55 + w^2*x^54 + x^53 + w*x^52 + x^51 + w^2*x^50 + x^49 + w^2*x^48 + x^47 + w^2*x^43 + x^41 + x^40 + w^2*x^39 + x^37 + w*x^36 + w^2*x^35 + w*x^33 + x^31 + w^2*x^30 + x^29 + w*x^28 + w
]
[2]:  [[85, 28, 13]] 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1|0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 1 0 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 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 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1|0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 0 0 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 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 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1]
      [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 1 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 0 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 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 1 1 1 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 1 0 1|0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 1 1 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 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 1 1 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1|0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 1 1 0 1 1 1 0 1 1 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 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1|0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0]
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      [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 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 0|0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 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 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0|0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1]
      [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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 0 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