Bounds on the minimum distance of additive quantum codes

Bounds on [[75,63]]2

lower bound:4
upper bound:4

Construction

Construction of a [[75,63,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[75, 63, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 9, 10, 13, 15, 18, 20, 22, 23, 24, 27, 28, 30, 32, 33, 39, 41, 42, 44, 47, 48, 49, 51, 55, 58, 62, 63, 68, 74, 75, 76, 78, 80, 86, 87, 88, 90, 91, 93, 101, 104, 108, 109, 116, 118, 120, 124, 125, 126 }

    stabilizer matrix:

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