Bounds on the minimum distance of additive quantum codes

Bounds on [[97,43]]2

lower bound:10
upper bound:18

Construction

Construction of a [[97,43,10]] quantum code:
[1]:  [[91, 43, 10]] quantum code over GF(2^2)
     cyclic code of length 91 with generating polynomial w^2*x^90 + x^89 + w*x^88 + x^87 + w*x^86 + w*x^85 + w^2*x^84 + x^83 + w*x^82 + x^81 + w*x^80 + x^79 + x^78 + x^76 + w^2*x^75 + w^2*x^74 + w^2*x^73 + w^2*x^72 + x^70 + w^2*x^68 + w^2*x^67 + w^2*x^66 + w^2*x^64 + w*x^62 + x^61 + x^59 + w*x^56 + w*x^55 + x^54 + x^53 + x^52 + w*x^51 + w^2*x^49 + x^48 + w*x^47 + w^2*x^46 + w^2*x^44 + x^43 + x^42 + w*x^41 + w*x^40 + w^2*x^39 + w^2*x^38 + w^2*x^37 + w^2*x^36 + x^35 + w*x^34 + w*x^32 + x^31 + w*x^30 + w*x^29 + w*x^28 + w*x^27 + w^2*x^26 + x^24 + 1
[2]:  [[97, 43, 10]] quantum code over GF(2^2)
     ExtendCode [1] by 6

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