Bounds on the minimum distance of additive quantum codes

Bounds on [[44,31]]2

lower bound:4
upper bound:4

Construction

Construction of a [[44,31,4]] quantum code:
[1]:  [[62, 50, 4]] Quantum code over GF(2^2)
     quasicyclic code of length 62 stacked to height 2 with 4 generating polynomials
[2]:  [[44, 32, 4]] Quantum code over GF(2^2)
     Shortening of [1] at { 9, 10, 13, 14, 20, 22, 36, 37, 38, 41, 44, 46, 47, 49, 50, 53, 57, 61 }
[3]:  [[44, 31, 4]] Quantum code over GF(2^2)
     Subcode of [2]

    stabilizer matrix:

      [1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1|0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0]
      [0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1|0 1 0 0 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0]
      [0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 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 1 0 1 0 1 1 0 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 0 0 1 1]
      [0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1|1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 0 1 1]
      [0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1|0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1]
      [0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1|1 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 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 1 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 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 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1|0 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 0 1 1 1 1 0 1 0|0 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0|0 0 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 1 0|0 1 1 0 1 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1|1 1 1 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 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 1 0 1 1 0 0 0 0 0 0 1 1|0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 1 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 (grassl@ira.uka.de). Last change: 23.10.2014