Bounds on the minimum distance of additive quantum codes

Bounds on [[78,65]]2

lower bound:4
upper bound:4

Construction

Construction of a [[78,65,4]] quantum code:
[1]:  [[78, 66, 4]] quantum code over GF(2^2)
     quasicyclic code of length 78 with 5 generating polynomials
[2]:  [[78, 65, 4]] quantum code over GF(2^2)
     Subcode of [1]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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