Bounds on the minimum distance of additive quantum codes

Bounds on [[76,55]]2

lower bound:5
upper bound:6

Construction

Construction of a [[76,55,5]] 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]:  [[76, 55, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 2, 7, 8, 11, 14, 16, 20, 21, 22, 24, 27, 28, 33, 35, 38, 41, 45, 46, 47, 48, 53, 54, 56, 58, 60, 61, 62, 64, 66, 67, 70, 73, 75, 78, 81, 86, 92, 93, 94, 100, 103, 104, 108, 111, 113, 114, 120, 121, 123, 124, 127 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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