Bounds on the minimum distance of additive quantum codes

Bounds on [[61,45]]2

lower bound:4
upper bound:5

Construction

Construction of a [[61,45,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[61, 45, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 9, 12, 13, 14, 17, 19, 20, 22, 23, 28, 33, 34, 56, 57, 59, 62, 64, 65, 71, 75, 76, 77, 78, 82 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


This page is maintained by Markus Grassl (grassl@ira.uka.de). Last change: 23.10.2014