Bounds on the minimum distance of additive quantum codes

Bounds on [[79,57]]2

lower bound:5
upper bound:7

Construction

Construction of a [[79,57,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[80, 57, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 5, 7, 8, 13, 14, 20, 21, 25, 31, 33, 35, 39, 41, 42, 47, 48, 49, 50, 52, 54, 60, 61, 69, 70, 71, 72, 73, 74, 81, 85, 88, 91, 95, 97, 102, 104, 107, 108, 112, 114, 115, 117, 120, 121, 123, 124, 125, 128 }
[3]:  [[79, 57, 5]] quantum code over GF(2^2)
     Puncturing of [2] at { 80 }

    stabilizer matrix:

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