Bounds on the minimum distance of additive quantum codes

Bounds on [[96,64]]2

lower bound:7
upper bound:10

Construction

Construction of a [[96,64,7]] quantum code:
[1]:  [[128, 96, 7]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[96, 64, 7]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 31, 38, 41, 43, 44, 45, 52, 53, 59, 62, 65, 66, 67, 70, 77, 78, 84, 88, 91, 92, 93, 98, 103, 110, 113, 115, 120, 121, 122, 124, 128 }

    stabilizer matrix:

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