Bounds on the minimum distance of additive quantum codes

Bounds on [[81,67]]2

lower bound:4
upper bound:4

Construction

Construction of a [[81,67,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[79, 67, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 4, 12, 13, 14, 17, 18, 20, 22, 23, 25, 27, 29, 33, 34, 38, 43, 44, 47, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 66, 67, 68, 71, 72, 73, 74, 78, 82, 87, 88, 90, 91, 102, 109, 111, 112, 115, 122 }
[3]:  [[81, 67, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 2

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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