Bounds on the minimum distance of additive quantum codes

Bounds on [[56,37]]2

lower bound:5
upper bound:6

Construction

Construction of a [[56,37,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[56, 38, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 7, 10, 11, 12, 14, 16, 20, 21, 23, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 48, 50, 56, 58, 61, 62, 65, 67, 68, 72, 78, 79, 81, 83, 84, 86, 87, 88, 89, 90, 94, 96, 98, 99, 100, 101, 104, 105, 106, 110, 112, 114, 116, 117, 118, 120, 122 }
[3]:  [[56, 37, 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 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1|0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1]
      [0 1 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 1 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0|1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 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 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0|1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1]
      [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 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0|0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 1 0 1]
      [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 0|1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0|0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 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 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0|0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 0 1 1]
      [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 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0 1 0 0|1 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 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 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1|0 1 0 1 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 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 1 1 1 1 1 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 1 1 1 1 0 1 0 1 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 1 0 0 1 1|0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 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 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1|0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 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 1 1 0 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0|0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 0|1 0 1 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 0|1 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 1 1 1 0 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 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0|1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0]
      [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 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 1 1|0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 1 1 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 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0|1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 1 1 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 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 1 0|1 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 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