Bounds on the minimum distance of additive quantum codes

Bounds on [[92,57]]2

lower bound:7
upper bound:11

Construction

Construction of a [[92,57,7]] quantum code:
[1]:  [[87, 57, 7]] quantum code over GF(2^2)
     quasicyclic code of length 87 stacked to height 2 with 6 generating polynomials
[2]:  [[92, 57, 7]] quantum code over GF(2^2)
     ExtendCode [1] by 5

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