Bounds on the minimum distance of additive quantum codes

Bounds on [[100,1]]2

lower bound:21
upper bound:33

Construction

Construction of a [[100,1,21]] quantum code:
[1]:  [[91, 1, 21]] quantum code over GF(2^2)
     cyclic code of length 91 with generating polynomials [
w*x^89 + x^88 + w^2*x^87 + w^2*x^86 + w*x^85 + w^2*x^84 + w*x^83 + x^82 + x^80 + x^79 + w*x^78 + x^76 + w*x^75 + w^2*x^73 + x^72 + x^71 + w*x^70 + w*x^69 + x^66 + x^65 + x^64 + x^63 + w^2*x^61 + w*x^60 + w^2*x^59 + w^2*x^58 + w^2*x^57 + w^2*x^55 + w^2*x^53 + w^2*x^52 + x^51 + w*x^50 + x^49 + w*x^48 + w^2*x^47 + x^46 + x^45 + 1,
w^2*x^89 + w*x^88 + x^87 + x^86 + w^2*x^85 + x^84 + w^2*x^83 + w*x^82 + w*x^80 + w*x^79 + w^2*x^78 + w*x^76 + w^2*x^75 + x^73 + w*x^72 + w*x^71 + w^2*x^70 + w^2*x^69 + w*x^66 + w*x^65 + w*x^64 + w*x^63 + x^61 + w^2*x^60 + x^59 + x^58 + x^57 + x^55 + x^53 + x^52 + w*x^51 + w^2*x^50 + w*x^49 + w^2*x^48 + x^47 + w*x^46 + w*x^45 + w
]
[2]:  [[100, 1, 21]] quantum code over GF(2^2)
     ExtendCode [1] by 9

    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 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 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 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 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 1 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 1 1 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 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
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last modified: 2006-04-09

Notes


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