Bounds on the minimum distance of additive quantum codes

Bounds on [[70,51]]2

lower bound:5
upper bound:6

Construction

Construction of a [[70,51,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[70, 52, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 5, 6, 7, 10, 11, 12, 17, 23, 26, 27, 28, 29, 32, 35, 37, 38, 41, 43, 44, 45, 49, 53, 56, 57, 58, 60, 63, 65, 70, 72, 74, 75, 77, 80, 89, 90, 91, 92, 93, 96, 98, 102, 105, 106, 108, 109, 111, 115, 119, 120, 121 }
[3]:  [[70, 51, 5]] quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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