Bounds on the minimum distance of additive quantum codes

Bounds on [[78,56]]2

lower bound:5
upper bound:7

Construction

Construction of a [[78,56,5]] 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]:  [[77, 56, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 1, 6, 11, 14, 16, 19, 20, 22, 23, 32, 33, 35, 39, 42, 43, 44, 46, 49, 50, 52, 55, 58, 62, 63, 68, 69, 70, 74, 76, 78, 79, 83, 85, 86, 90, 92, 97, 100, 104, 105, 110, 111, 112, 113, 120, 121, 122, 123, 124, 127 }
[4]:  [[78, 56, 5]] quantum code over GF(2^2)
     ExtendCode [3] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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