Bounds on the minimum distance of additive quantum codes

Bounds on [[55,36]]2

lower bound:5
upper bound:6

Construction

Construction of a [[55,36,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[54, 36, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 3, 4, 5, 6, 8, 11, 13, 14, 17, 20, 22, 23, 25, 26, 27, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 43, 47, 49, 50, 51, 54, 55, 56, 57, 58, 59, 60, 64, 65, 66, 67, 68, 70, 72, 74, 76, 78, 80, 81, 82, 83, 84, 86, 88, 91, 92, 98, 100, 101, 104, 106, 108, 115, 116, 117, 118, 120 }
[3]:  [[55, 36, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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