Bounds on the minimum distance of additive quantum codes

Bounds on [[84,75]]2

lower bound:3
upper bound:3

Construction

Construction of a [[84,75,3]] quantum code:
[1]:  [[128, 119, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[84, 75, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 6, 7, 8, 13, 15, 18, 22, 25, 26, 28, 29, 32, 35, 39, 40, 43, 48, 55, 61, 63, 69, 77, 78, 82, 83, 92, 95, 98, 101, 103, 106, 112, 113, 114, 116, 118, 119, 120, 121, 122, 124, 125 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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