Bounds on the minimum distance of additive quantum codes

Bounds on [[90,76]]2

lower bound:4
upper bound:4

Construction

Construction of a [[90,76,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[88, 76, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 5, 6, 12, 14, 31, 35, 36, 51, 55, 56, 58, 59, 61, 63, 72, 77, 78, 83, 85, 87, 89, 90, 91, 93, 94, 97, 99, 100, 101, 102, 106, 109, 111, 113, 114, 115, 121, 125 }
[3]:  [[90, 76, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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