Bounds on the minimum distance of additive quantum codes

Bounds on [[74,53]]2

lower bound:5
upper bound:7

Construction

Construction of a [[74,53,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[127, 106, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 128
[3]:  [[74, 53, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 2, 6, 8, 11, 12, 13, 17, 20, 24, 25, 26, 28, 32, 37, 38, 40, 44, 50, 54, 55, 56, 57, 59, 60, 61, 63, 64, 65, 70, 71, 73, 76, 77, 78, 79, 80, 89, 90, 91, 92, 94, 97, 98, 99, 100, 104, 105, 106, 114, 120, 121, 123, 126 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014