Bounds on the minimum distance of additive quantum codes

Bounds on [[64,46]]2

lower bound:5
upper bound:6

Construction

Construction of a [[64,46,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[64, 46, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 3, 4, 8, 9, 10, 13, 14, 18, 19, 20, 21, 22, 24, 27, 29, 30, 31, 32, 33, 34, 35, 37, 40, 42, 43, 45, 49, 53, 54, 55, 57, 60, 61, 62, 66, 69, 70, 73, 75, 77, 79, 80, 83, 85, 87, 92, 94, 99, 100, 104, 107, 109, 110, 111, 113, 117, 119, 120 }

    stabilizer matrix:

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