Bounds on the minimum distance of additive quantum codes

Bounds on [[83,71]]2

lower bound:4
upper bound:4

Construction

Construction of a [[83,71,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[83, 71, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 6, 8, 9, 16, 17, 18, 28, 29, 32, 34, 35, 40, 41, 44, 47, 48, 52, 53, 58, 59, 62, 69, 72, 74, 77, 78, 81, 91, 93, 98, 99, 104, 107, 109, 110, 111, 114, 116, 117, 119, 121, 125 }

    stabilizer matrix:

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