Bounds on the minimum distance of additive quantum codes

Bounds on [[58,39]]2

lower bound:5
upper bound:6

Construction

Construction of a [[58,39,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[58, 40, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 5, 6, 9, 10, 13, 14, 18, 19, 23, 25, 26, 33, 34, 35, 37, 38, 39, 42, 45, 47, 48, 50, 51, 53, 54, 55, 56, 57, 58, 60, 62, 67, 70, 72, 74, 75, 76, 79, 80, 81, 82, 84, 85, 86, 87, 89, 91, 92, 97, 98, 99, 102, 103, 105, 106, 107, 109, 110, 111, 116, 117, 119, 120, 121 }
[3]:  [[58, 39, 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 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0|0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 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 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1|0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 1|1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 1]
      [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0|1 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 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 1 1 1 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 1 0 1|1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 0 1 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1|1 0 1 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 1 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 1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 0|0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 1]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0|0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 1 0 0 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 0 1 0 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0|1 0 1 0 1 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 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 0 0 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 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 1 0 1 0 1 0 0 1 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 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0|1 1 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 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 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0|1 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 1 0 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 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 1 1 0 0|1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 0 1]
      [0 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 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 0|0 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 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 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 0 0|0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0|1 0 1 1 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 0 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 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 1|0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 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 1 1 1 0 1 1 0 0 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 0 0|0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 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 0 1 0 1 1 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 0 0 1|0 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 0 1 1 0]

last modified: 2006-04-03

Notes


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