Bounds on the minimum distance of additive quantum codes

Bounds on [[88,67]]2

lower bound:5
upper bound:6

Construction

Construction of a [[88,67,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[127, 106, 5]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at 128
[3]:  [[88, 67, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 4, 9, 10, 14, 16, 20, 23, 24, 27, 33, 44, 46, 50, 53, 55, 57, 59, 61, 65, 66, 68, 70, 71, 75, 81, 83, 85, 86, 93, 95, 103, 104, 105, 106, 107, 118, 120, 121, 125 }

    stabilizer matrix:

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