Bounds on the minimum distance of additive quantum codes

Bounds on [[90,81]]2

lower bound:3
upper bound:3

Construction

Construction of a [[90,81,3]] quantum code:
[1]:  [[128, 119, 3]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[90, 81, 3]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 4, 5, 6, 9, 13, 16, 18, 22, 23, 30, 31, 32, 35, 36, 37, 46, 51, 53, 66, 67, 69, 75, 78, 86, 87, 96, 100, 105, 107, 109, 114, 115, 117, 123, 125, 127 }

    stabilizer matrix:

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