Bounds on the minimum distance of additive quantum codes

Bounds on [[103,85]]2

lower bound:4
upper bound:6

Construction

Construction of a [[103,85,4]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[102, 84, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 44, 62, 69, 79, 80, 82, 83, 92, 95, 96, 97, 102, 105, 107, 109, 110, 114, 115, 119, 122 }
[3]:  [[101, 85, 4]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [2] at 102
[4]:  [[103, 85, 4]] quantum code over GF(2^2)
     ExtendCode [3] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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