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ACS Searching for D4t-Hadamard Matrices

  • Víctor Álvarez
  • José Andrés Armario
  • María Dolores Frau
  • Félix Gudiel
  • Belén Güemes
  • Elena Martín
  • Amparo Osuna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6234)

Abstract

An Ant Colony System (ACS) looking for cocyclic Hadamard matrices over dihedral groups D 4t is described. The underlying weighted graph consists of the rooted trees described in [1], whose vertices are certain subsets of coboundaries. A branch of these trees defines a D 4t -Hadamard matrix if and only if two conditions hold: (i) I i  = i − 1 and, (ii) c i  = t, for every 2 ≤ i ≤ t, where I i and c i denote the number of i-paths and i-intersections (see [3] for details) related to the coboundaries defining the branch. The pheromone and heuristic values of our ACS are defined in such a way that condition (i) is always satisfied, and condition (ii) is closely to be satisfied.

Keywords

Cocyclic Hadamard matrix ant colony system i-path i-intersection 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Víctor Álvarez
    • 1
  • José Andrés Armario
    • 1
  • María Dolores Frau
    • 1
  • Félix Gudiel
    • 1
  • Belén Güemes
    • 1
  • Elena Martín
    • 1
  • Amparo Osuna
    • 1
  1. 1.University of SevillaSevillaSpain

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