Bounds on the minimum distance of additive quantum codes

Bounds on [[81,69]]2

lower bound:4
upper bound:4

Construction

Construction of a [[81,69,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[81, 69, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 6, 14, 16, 18, 29, 33, 34, 36, 38, 40, 41, 42, 44, 50, 59, 60, 61, 67, 77, 80, 81, 82, 83, 85, 92, 93, 95, 97, 100, 101, 102, 107, 108, 109, 110, 112, 115, 116, 117, 121, 122 }

    stabilizer matrix:

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