Bounds on the minimum distance of additive quantum codes

Bounds on [[57,41]]2

lower bound:4
upper bound:6

Construction

Construction of a [[57,41,4]] quantum code:
[1]:  [[85, 69, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 85 with 4 generating polynomials
[2]:  [[57, 41, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 6, 7, 9, 10, 12, 13, 23, 25, 27, 33, 34, 37, 41, 44, 45, 50, 51, 59, 62, 63, 64, 67, 70, 71, 72, 75, 84 }

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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