Bounds on the minimum distance of additive quantum codes

Bounds on [[83,68]]2

lower bound:4
upper bound:5

Construction

Construction of a [[83,68,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[80, 68, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 3, 4, 8, 10, 11, 14, 16, 19, 20, 23, 24, 25, 30, 31, 33, 42, 44, 47, 49, 51, 52, 55, 57, 58, 61, 63, 68, 74, 80, 84, 85, 87, 92, 98, 99, 109, 113, 114, 116, 117, 118, 119, 120, 124 }
[3]:  [[83, 68, 4]] quantum code over GF(2^2)
     ExtendCode [2] by 3

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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