Bounds on the minimum distance of additive quantum codes

Bounds on [[40,17]]2

lower bound:6
upper bound:8

Construction

Construction of a [[40,17,6]] quantum code:
[1]:  [[70, 48, 5]] Quantum code over GF(2^2)
     quasicyclic code of length 70 stacked to height 2 with 4 generating polynomials
[2]:  [[40, 18, 6]] Quantum code over GF(2^2)
     Shortening of [1] at { 1, 2, 6, 8, 9, 13, 15, 16, 20, 22, 23, 27, 29, 30, 34, 37, 38, 42, 44, 45, 49, 51, 52, 56, 58, 59, 63, 65, 66, 70 }
[3]:  [[40, 17, 6]] Quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

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

last modified: 2006-04-03

Notes


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