Bounds on the minimum distance of additive quantum codes

Bounds on [[100,78]]2

lower bound:5
upper bound:6

Construction

Construction of a [[100,78,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[127, 106, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 128
[3]:  [[99, 78, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 11, 16, 20, 21, 29, 32, 33, 38, 41, 48, 62, 67, 70, 71, 75, 78, 84, 89, 92, 93, 96, 100, 104, 106, 108, 114, 123, 127 }
[4]:  [[100, 78, 5]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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