Bounds on the minimum distance of additive quantum codes

Bounds on [[60,41]]2

lower bound:5
upper bound:6

Construction

Construction of a [[60,41,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[60, 42, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 7, 11, 13, 15, 17, 18, 19, 20, 21, 22, 24, 27, 29, 30, 33, 34, 38, 40, 41, 46, 47, 48, 50, 51, 52, 54, 56, 58, 59, 60, 62, 63, 64, 67, 68, 69, 70, 72, 76, 78, 79, 80, 81, 82, 87, 88, 89, 90, 91, 92, 93, 97, 102, 104, 105, 106, 107, 114, 115, 116, 117, 120 }
[3]:  [[60, 41, 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 0 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0|0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 1 0 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 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1|0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 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 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 0 1|1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0|0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 0]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 1 0|0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0]
      [0 0 0 0 0 1 0 0 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 0 0 0 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0|1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 1 1 0 1 1 1 0 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 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 1 0|1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0|1 1 0 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 0 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 0 0 0 0 0 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 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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]
      [0 0 0 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 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 0 1|0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0|1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0|0 0 1 1 1 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 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 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0|0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0|0 0 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1|1 0 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1|1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 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 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 1 0 0 1|1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 1 1 0 1]
      [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 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0|1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 0 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 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0|0 1 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1]

last modified: 2006-04-03

Notes


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