Bounds on the minimum distance of additive quantum codes

Bounds on [[74,54]]2

lower bound:5
upper bound:6

Construction

Construction of a [[74,54,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[72, 54, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 9, 13, 14, 16, 17, 25, 28, 32, 33, 35, 38, 39, 49, 51, 55, 56, 58, 62, 66, 67, 68, 69, 70, 71, 72, 75, 79, 82, 84, 85, 87, 91, 94, 99, 100, 101, 103, 105, 108, 109, 111, 112, 113, 114, 116, 119, 121 }
[3]:  [[74, 54, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

      [1 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 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0|1 1 0 0 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 0 1 1 1 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 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0|1 0 0 0 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0|1 0 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0]
      [0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0|1 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 1 1 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 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 0 0|0 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 1 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 1 0 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0|1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0|0 1 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0]
      [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0|0 0 1 1 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0]
      [0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 1 0 1 0 0|0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 1 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 0 0 1 0 0 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0|1 0 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 0|0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0|1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0|0 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 0 0]
      [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 0 0 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0|1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0|0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 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 1 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0|0 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 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 0 1 0 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0|1 1 0 0 0 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 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 0 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0|0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 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 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 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 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 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 (codes@codetables.de). Last change: 23.10.2014