Bounds on the minimum distance of additive quantum codes

Bounds on [[72,51]]2

lower bound:5
upper bound:7

Construction

Construction of a [[72,51,5]] 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]:  [[72, 51, 5]] quantum code over GF(2^2)
     Shortening of [2] at { 1, 4, 6, 10, 11, 12, 13, 16, 19, 23, 24, 25, 29, 30, 31, 33, 35, 36, 41, 42, 43, 46, 48, 49, 53, 56, 57, 61, 62, 65, 66, 67, 75, 77, 79, 80, 84, 85, 89, 92, 93, 94, 98, 102, 108, 109, 110, 113, 114, 116, 117, 121, 122, 124, 125 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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