Bounds on the minimum distance of additive quantum codes

Bounds on [[68,4]]2

lower bound:15
upper bound:22

Construction

Construction of a [[68,4,15]] quantum code:
[1]:  [[72, 0, 18]] self-dual quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[68, 4, 15]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 1, 3, 14, 16 }

    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 1 0 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 0 0 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1|1 1 1 0 1 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1]
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      [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 0 0 0 0 0 0 1 0 0 1 1|0 0 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0]
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last modified: 2006-04-07

Notes


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