Bounds on the minimum distance of additive quantum codes

Bounds on [[79,31]]2

lower bound:10
upper bound:17

Construction

Construction type: Gra

Construction of a [[79,31,10]] quantum code:
[1]:  [[79, 31, 10]] quantum code over GF(2^2)
     random linear code
Construction from a stored generator matrix

    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 1 0 0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0|1 1 0 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 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 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 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 1|1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1|1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 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 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 0 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0|1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 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 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 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0|1 0 0 1 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 0 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 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 0 0|1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 1 0|0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 0 1 1 1 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 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 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 1 1 0|0 1 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 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 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1|0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0|1 1 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 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 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 1 1 0 1 1 1 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 1|1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0|0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 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 1 0 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0|1 0 1 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1 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 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1|1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 1 1]
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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 1 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 0 1 0 1 0|0 1 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 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 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 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0|0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 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 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 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0|0 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 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 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 0 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 1 1|0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 0 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 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 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1|0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1]
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last modified: 2022-08-04

Notes


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