Bounds on the minimum distance of additive quantum codes

Bounds on [[103,88]]2

lower bound:4
upper bound:4

Construction

Construction of a [[103,88,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[100, 88, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 3, 10, 12, 29, 47, 61, 80, 83, 94, 95, 96, 98, 99, 101, 102, 108, 111, 112, 113, 114, 117, 119, 120, 122, 123, 124 }
[3]:  [[103, 88, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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