Bounds on the minimum distance of additive quantum codes

Bounds on [[89,15]]2

lower bound:16
upper bound:26

Construction

Construction of a [[89,15,16]] quantum code:
[1]:  [[85, 17, 16]] quantum code over GF(2^2)
     cyclic code of length 85 with generating polynomials [
x^84 + w^2*x^83 + x^82 + w^2*x^80 + w^2*x^79 + x^78 + w^2*x^77 + x^75 + x^73 + w^2*x^72 + w*x^70 + w^2*x^69 + w*x^67 + w*x^66 + w^2*x^65 + w*x^64 + x^61 + w^2*x^60 + w^2*x^59 + w^2*x^58 + x^57 + w^2*x^56 + x^55 + x^54 + w*x^53 + w^2*x^51 + w*x^50 + w^2*x^49 + w^2*x^48 + w^2*x^45 + x^44 + w*x^43 + w*x^42 + w*x^41 + w*x^39 + w*x^37 + w^2*x^36 + w*x^35 + x^34 + 1,
w*x^84 + x^83 + w*x^82 + x^80 + x^79 + w*x^78 + x^77 + w*x^75 + w*x^73 + x^72 + w^2*x^70 + x^69 + w^2*x^67 + w^2*x^66 + x^65 + w^2*x^64 + w*x^61 + x^60 + x^59 + x^58 + w*x^57 + x^56 + w*x^55 + w*x^54 + w^2*x^53 + x^51 + w^2*x^50 + x^49 + x^48 + x^45 + w*x^44 + w^2*x^43 + w^2*x^42 + w^2*x^41 + w^2*x^39 + w^2*x^37 + x^36 + w^2*x^35 + w*x^34 + w
]
[2]:  [[85, 15, 16]] quantum code over GF(2^2)
     Subcode of [1]
[3]:  [[89, 15, 16]] quantum code over GF(2^2)
     ExtendCode [2] 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 0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 0 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 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 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 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 0 0 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 1 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1 0 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 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 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 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 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 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 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 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 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 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 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 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 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 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 0 0 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 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 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 1 0 0 0 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 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 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 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 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 1 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 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 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 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 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1 0 0 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 0 0 0 0 0 0 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 1 0 1 1 0 1 0 0 1 1 1 0 1 0 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 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 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 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 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 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 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 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 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 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 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 1 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 0 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 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 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 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 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 0 1 0 1 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 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 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