Bounds on the minimum distance of additive quantum codes

Bounds on [[53,34]]2

lower bound:5
upper bound:6

Construction

Construction of a [[53,34,5]] quantum code:
[1]:  [[122, 104, 5]] Quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[52, 34, 5]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 24, 25, 26, 30, 31, 32, 33, 36, 37, 40, 41, 42, 43, 44, 47, 49, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 74, 77, 80, 82, 84, 86, 87, 88, 94, 97, 98, 99, 100, 101, 102, 103, 110, 111, 115 }
[3]:  [[53, 34, 5]] Quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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