Bounds on the minimum distance of additive quantum codes

Bounds on [[75,51]]2

lower bound:6
upper bound:8

Construction

Construction of a [[75,51,6]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[74, 51, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 3, 4, 9, 10, 11, 14, 16, 17, 19, 23, 24, 26, 27, 28, 30, 31, 33, 37, 40, 42, 48, 55, 57, 59, 61, 63, 64, 66, 67, 69, 71, 72, 76, 78, 80, 82, 84, 85, 87, 97, 99, 100, 103, 104, 105, 110, 113, 115, 116, 118, 124, 125, 126 }
[3]:  [[75, 51, 6]] quantum code over GF(2^2)
     ExtendCode [2] by 1

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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