Bounds on the minimum distance of additive quantum codes

Bounds on [[90,75]]2

lower bound:4
upper bound:4

Construction

Construction of a [[90,75,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[87, 75, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 4, 12, 18, 20, 21, 25, 31, 37, 41, 43, 51, 58, 59, 60, 62, 67, 68, 69, 75, 78, 79, 82, 84, 85, 86, 90, 91, 92, 96, 97, 103, 104, 105, 107, 109, 113, 122, 123 }
[3]:  [[90, 75, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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