Bounds on the minimum distance of additive quantum codes

Bounds on [[95,25]]2

lower bound:15
upper bound:24

Construction

Construction of a [[95,25,15]] quantum code:
[1]:  [[91, 25, 15]] quantum code over GF(2^2)
     cyclic code of length 91 with generating polynomials [
w*x^89 + x^87 + w^2*x^85 + w*x^84 + w^2*x^83 + w*x^82 + w*x^80 + w^2*x^79 + w*x^78 + w*x^77 + w^2*x^76 + w*x^75 + w*x^74 + w*x^72 + x^71 + w*x^70 + w*x^69 + w*x^68 + w^2*x^66 + x^65 + x^63 + x^62 + w*x^61 + x^60 + x^59 + w^2*x^56 + x^55 + w^2*x^54 + w*x^53 + w*x^52 + w*x^51 + x^49 + x^48 + w^2*x^47 + w^2*x^45 + w^2*x^44 + w*x^42 + w^2*x^41 + w^2*x^40 + w^2*x^38 + w*x^36 + w^2*x^34 + x^33 + 1,
w^2*x^89 + w*x^87 + x^85 + w^2*x^84 + x^83 + w^2*x^82 + w^2*x^80 + x^79 + w^2*x^78 + w^2*x^77 + x^76 + w^2*x^75 + w^2*x^74 + w^2*x^72 + w*x^71 + w^2*x^70 + w^2*x^69 + w^2*x^68 + x^66 + w*x^65 + w*x^63 + w*x^62 + w^2*x^61 + w*x^60 + w*x^59 + x^56 + w*x^55 + x^54 + w^2*x^53 + w^2*x^52 + w^2*x^51 + w*x^49 + w*x^48 + x^47 + x^45 + x^44 + w^2*x^42 + x^41 + x^40 + x^38 + w^2*x^36 + x^34 + w*x^33 + w
]
[2]:  [[95, 25, 15]] quantum code over GF(2^2)
     ExtendCode [1] by 4

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