Bounds on the minimum distance of additive quantum codes

Bounds on [[104,90]]2

lower bound:4
upper bound:4

Construction

Construction of a [[104,90,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[102, 90, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 18, 61, 83, 95, 96, 97, 99, 101, 102, 103, 105, 106, 109, 111, 112, 113, 114, 119, 120, 123, 124, 126 }
[3]:  [[104, 90, 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 1 0 1 0 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 0|0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0]
      [0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0|0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0]
      [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 0 0 0|0 0 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 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 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0]
      [0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0|0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 1 0 0]
      [0 0 0 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0|0 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0]
      [0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0|0 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0]
      [0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0|0 1 1 1 0 1 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 0]
      [0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0|0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0]
      [0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0 0 0|0 1 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 1 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 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 0 0|0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 1 0 0 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 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 0 0|0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 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 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 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 0 0 0 0 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 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 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 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 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