Bounds on the minimum distance of additive quantum codes

Bounds on [[75,52]]2

lower bound:5
upper bound:8

Construction

Construction of a [[75,52,5]] quantum code:
[1]:  [[128, 105, 6]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[76, 53, 6]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 3, 4, 5, 7, 10, 11, 12, 16, 19, 20, 21, 22, 25, 26, 28, 29, 30, 31, 38, 40, 51, 54, 57, 60, 61, 62, 63, 66, 68, 69, 71, 73, 77, 80, 84, 90, 95, 102, 105, 106, 107, 108, 111, 112, 114, 115, 116, 118, 122, 123, 126 }
[3]:  [[76, 52, 6]] quantum code over GF(2^2)
     Subcode of [2]
[4]:  [[75, 52, 5]] quantum code over GF(2^2)
     Puncturing of [3] at { 76 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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