Bounds on the minimum distance of additive quantum codes

Bounds on [[78,58]]2

lower bound:5
upper bound:6

Construction

Construction of a [[78,58,5]] quantum code:
[1]:  [[122, 104, 5]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[76, 58, 5]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 16, 20, 21, 23, 24, 25, 28, 29, 32, 33, 36, 37, 39, 40, 42, 46, 52, 57, 58, 60, 71, 72, 74, 81, 85, 88, 91, 93, 95, 96, 98, 99, 100, 104, 106, 107, 108, 111, 112, 116, 117, 118, 119, 120, 122 }
[3]:  [[78, 58, 5]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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