Bounds on the minimum distance of additive quantum codes

Bounds on [[72,60]]2

lower bound:4
upper bound:4

Construction

Construction of a [[72,60,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[72, 60, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 6, 8, 13, 15, 17, 18, 23, 24, 26, 27, 31, 33, 34, 35, 40, 42, 45, 52, 53, 54, 59, 62, 64, 65, 66, 68, 72, 73, 74, 76, 77, 78, 80, 81, 82, 86, 90, 93, 95, 96, 99, 101, 104, 105, 108, 111, 113, 116, 118, 121, 122, 124, 126 }

    stabilizer matrix:

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