Bounds on the minimum distance of additive quantum codes

Bounds on [[73,52]]2

lower bound:5
upper bound:7

Construction

Construction of a [[73,52,5]] 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]:  [[73, 52, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 2, 5, 6, 7, 10, 11, 12, 13, 14, 15, 20, 22, 24, 27, 29, 37, 38, 39, 41, 44, 47, 48, 49, 51, 52, 53, 54, 55, 57, 67, 71, 74, 76, 79, 80, 82, 84, 85, 93, 95, 100, 101, 105, 107, 112, 113, 114, 116, 117, 118, 121, 124, 126, 127 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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