Bounds on the minimum distance of additive quantum codes

Bounds on [[121,107]]2

lower bound:4
upper bound:4

Construction

Construction of a [[121,107,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[120, 108, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 61, 83, 98, 101, 114, 117 }
[3]:  [[120, 107, 4]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[121, 107, 4]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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