Bounds on the minimum distance of additive quantum codes

Bounds on [[80,43]]2

lower bound:8
upper bound:12

Construction

Construction of a [[80,43,8]] quantum code:
[1]:  [[128, 91]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[80, 43, 8]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 6, 8, 12, 16, 17, 19, 26, 28, 31, 35, 37, 38, 39, 44, 45, 46, 49, 51, 52, 53, 61, 63, 68, 73, 76, 80, 89, 90, 91, 92, 94, 95, 97, 99, 100, 104, 105, 107, 111, 112, 117, 119, 121, 122, 123, 125, 127 }

    stabilizer matrix:

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