Bounds on the minimum distance of additive quantum codes

Bounds on [[93,81]]2

lower bound:4
upper bound:4

Construction

Construction of a [[93,81,4]] quantum code:
[1]:  [[126, 114, 4]] quantum code over GF(2^2)
     Construction from a stored generator matrix
[2]:  [[93, 81, 4]] quantum code over GF(2^2)
     Shortening of [1] at { 2, 12, 13, 18, 20, 29, 47, 61, 80, 83, 94, 95, 97, 99, 100, 101, 103, 106, 107, 109, 110, 111, 113, 115, 116, 117, 118, 119, 121, 123, 124, 125, 126 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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