Bounds on the minimum distance of additive quantum codes

Bounds on [[99,67]]2

lower bound:6
upper bound:10

Construction

Construction of a [[99,67,6]] quantum code:
[1]:  [[99, 66, 7]] quantum code over GF(2^2)
     quasicyclic code of length 99 with 2 generating polynomials
[2]:  [[98, 67, 6]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 99
[3]:  [[99, 67, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 1

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