HadamardSearch

This is a tool for looking for cocyclic Hadamard matrices over a finite group G for which a homological model hG is known, as described by V.Alvarez, J.A.Armario, M.D.Frau and P.Real in ”Calculating cocyclic Hadamard matrices in Mathematica: exhaustive and heuristic searches”, ICMS-06, Castro Urdiales, Spain (2006). To appear in a special issue of LNCS. Two searching methods are provided. The exhaustive one developes a full search among all 2-cocycles. The heuristic search consists in a genetic algorithm, described by V.Alvarez, J.A.Armario, M.D.Frau and P.Real in ”A genetic algorithm for cocyclic Hadamard matrices”, AAECC-16, Las Vegas, USA, LNCS 3857, 144--153 (2006). Six input data are needed: 1. A matrix PR representing the group law on G. 2. A matrix M2 representing the differential d2 on hG_2. 3. A matrix M3 representing the differential d3 on hG_3. 4. A matrix F1 representing the projection from B_1(Z[G]) to hG_1. 5. A matrix F2 representing the projection from B_2(Z[G]) to hG_2. 6. 1 for developing an exhaustive search, anything else for developing a heuristic search.


References in zbMATH (referenced in 10 articles )

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  1. Alvarez, V.; Armario, J. A.; Falcón, R. M.; Frau, M. D.; Gudiel, F.; Güemes, M. B.; Osuna, A.: A mixed heuristic for generating cocyclic Hadamard matrices (2018)
  2. Álvarez, V.; Armario, J. A.; Frau, M. D.; Real, P.: On higher dimensional cocyclic Hadamard matrices (2015)
  3. Alvarez, Victor; Armario, Jose Andres; Frau, Maria Dolores; Guidiel, Felix: Embedding cocylic (D)-optimal designs in cocylic Hadamard matrices (2012)
  4. Álvarez, Víctor; Armario, José Andrés; Frau, María Dolores; Real, Pedro: Homological models for semidirect products of finitely generated Abelian groups. (2012)
  5. Alvarez, V.; Armario, J. A.; Frau, M. D.; Real, P.: The homological reduction method for computing cocyclic Hadamard matrices (2009)
  6. Álvarez, Víctor; Armario, José Ándrés; Frau, María Dolores; Gudiel, Félix; Osuna, Amparo: Rooted trees searching for cocyclic Hadamard matrices over (D_4t) (2009)
  7. Álvarez, V.; Armario, J. A.; Frau, M. D.; Real, P.: A system of equations for describing cocyclic Hadamard matrices (2008)
  8. Álvarez, V.; Armario, J. A.; Frau, M. D.; Real, P.: Calculating cocyclic Hadamard matrices in Mathematica: exhaustive and heuristic searches (2006)
  9. Álvarez, V.; Armario, J. A.; Frau, M. D.; Real, P.: A genetic algorithm for cocyclic Hadamard matrices (2006)
  10. Iglesias, Andrés (ed.); Takayama, Nobuki (ed.): Mathematical software -- ICMS 2006. Second international congress on mathematical software, Castro Urdiales, Spain, September 1--3, 2006. Proceedings (2006)