Bounds on the minimum distance of additive quantum codes

Bounds on [[78,57]]2

lower bound:5
upper bound:6

Construction

Construction of a [[78,57,5]] 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]:  [[78, 57, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 3, 4, 5, 6, 8, 9, 11, 17, 18, 23, 24, 25, 29, 31, 33, 34, 35, 40, 42, 49, 53, 54, 61, 64, 66, 68, 71, 72, 74, 76, 85, 87, 88, 89, 92, 95, 96, 97, 98, 100, 103, 105, 107, 108, 109, 112, 113, 118, 125 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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