Bounds on the minimum distance of additive quantum codes

Bounds on [[62,43]]2

lower bound:5
upper bound:6

Construction

Construction of a [[62,43,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[62, 44, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 9, 13, 14, 16, 17, 24, 25, 28, 32, 33, 35, 38, 39, 49, 51, 55, 56, 58, 62, 66, 67, 68, 69, 70, 71, 72, 74, 76, 77, 78, 79, 80, 82, 83, 85, 86, 89, 91, 93, 95, 96, 97, 98, 99, 100, 104, 105, 107, 108, 109, 112, 113, 115, 118, 120, 121, 122 }
[3]:  [[62, 43, 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 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 0|1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0]
      [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0|1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 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 1 1 1 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0|1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1|1 1 0 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0|0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 0 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 1 1 1 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0|1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 1 0 0 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 1 1 0 1 1 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 0 0 0|0 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 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 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0|0 0 0 1 1 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 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 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 0 1 0 0 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 1 1|1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 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 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1|0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 1 0 0 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 0 1 1 1|1 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 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 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 1|0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 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 0 0 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 1|0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 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 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0|1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0|0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 0|0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0|1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 0 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 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 0 0 1 0 0 0 1 0 0 1|0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 1 0 0]

last modified: 2006-04-03

Notes


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