Bounds on the minimum distance of additive quantum codes

Bounds on [[50,32]]2

lower bound:5
upper bound:6

Construction

Construction of a [[50,32,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[50, 32, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 18, 19, 22, 23, 24, 25, 26, 28, 29, 31, 32, 35, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 54, 55, 56, 58, 59, 62, 64, 65, 66, 69, 70, 71, 72, 75, 76, 78, 81, 82, 84, 87, 91, 93, 94, 97, 98, 100, 103, 104, 105, 106, 107, 113, 114, 115, 117, 121, 122 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014