Bounds on the minimum distance of additive quantum codes

Bounds on [[73,47]]2

lower bound:6
upper bound:8

Construction

Construction of a [[73,47,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[70, 47, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 7, 8, 9, 10, 13, 14, 15, 21, 22, 24, 25, 26, 27, 29, 30, 33, 34, 37, 38, 42, 43, 45, 51, 53, 56, 57, 61, 63, 65, 67, 76, 79, 80, 82, 84, 86, 89, 92, 93, 94, 95, 97, 98, 99, 102, 103, 107, 108, 109, 110, 112, 116, 119, 121, 125, 126 }
[3]:  [[73, 47, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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